CURRICULUM VITA                                      

          Gilbert G. Walter                     2122 E. Edgewood Avenue 
                                                Milwaukee, WI   53211 
                                                Telephone:  (414) 964-8711 

                                     Professor Emeritus of Mathematics 
                                     Department of Mathematical Sciences 
                                     University of Wisconsin-Milwaukee 
                                     P.O. Box 413 Milwaukee, WI  53201 

                                                Telephone:  (414) 229-5528 
                                                Fax:  (414) 229-4907 


     Born in 1930 in the bucolic little town of Ottawa, Illinois of German
     immigrant parents, I soon showed promise of things to come.  At the age
     of five I tried to catch a ball thrown by my father and dropped it. 
     Later when he tried teaching me to ride a bicycle, I kept falling off.

Later, my parents moved to the suburbs of Chicago where I eventually attended
Riverside-Brookfield High School. When I failed to make the track team
(or any other team), I realized my dream of athletic greatness was not to be
realized.  It was then that I turned to mathematics which was considered a
sissy subject suitable mainly for girls.  Since many attractive girls took
the subject and looked to me for help, I decided mathematics was something
to pursue.  Thus a career was born.

     Well, not quite.  I studied industrial engineering at General Motors
     Institute, was drafted by the Army, studied electrical engineering at
     Mew Mexico State University, and came to Milwaukee to practice my new
     trade.  While working at AC Electronics, I took a night school course
     in mathematics from Morris Marden.  He suggested I go to graduate school
     in mathematics and obtained an offer of a teaching assistantship for me
     in Madison.  Since my work at AC, though interesting, was likely to blow
     up (I worked on bombs), I decided to take the offer.

                     My next four years as a graduate student were
                     uneventful (except for my marriage and the birth of
		     my three children).  When my major professor, Jacob
		     Korevaar, left for a year's leave, I took a temporary
		     job in Milwaukee while writing my dissertation. 
		     I have been here since.  

                 Well, not quite.  I have taken every opportunity to visit
		 warmer places beginning with the University of
		 California-San Diego and ending with the Arizona State University

          Education:      BIE       General Motors Institute, 1953 
                          BSEE      New Mexico State University, 1956 
                          MS        (Mathematics) University of Wisconsin, 1959 
                          Ph.D.     (Mathematics, EE Minor), University of 
			             Wisconsin, 1962 


          1961-present        Instructor to Professor, Mathematical 
                              Sciences, University of Wisconsin-Milwaukee
                              (Chair 1973-1975) (1993-1995)(Retired 1999).

	  Spring 1999	      Visitor, Arizona State University
          1995-1996           Visiting Colleague, University of Hawaii

          Fall 1987           Visiting Professor, University of Delaware 

          Winter 1985         Visiting Mathematician, Centro de  
                              Investigaciones e Estudios Avanzados,
                              IPN, Merida, Mexico

          Spring 1985         Visiting Professor, California 
                              Polytechnic., San Luis Obispo, California

          Spring 1981         Visiting Professor, University of California-

          Winter 1981         Visitor, Inst. Ivest. Mat. Appl. and Syst.,
                              UNAM, Mexico City 

          Fall 1980           Visitor, Imperial College, London 

          Summer 1979         Visiting Professor, University of Costa Rica 

          Summer 1974,        Visiting Mathematician, Nat. Mar. Fish. 
          1975, 1976          Service, NOAA, Woods Hole, Mass. 

          1968-1969           Visiting Associate Professor, Universidad 
                              Agraria, Lima, Peru 

          1965-1966           Visiting Assistant Professor, University of  
                              California-San Diego 

          1956-1957           Project Engineer, AC Electronics, Milwaukee 

          1953-1955           U.S. Army 

          1952-1953           Jr. Project Engineer, Electro-Motive Div. GM, 
                              LaGrange, IL 

          Other Academic Activities: 

          I.  Teaching Experience: 

              a)  Undergraduate:   Basic   statistics, differential equations,  
                  mathematical  statistics, linear algebra, time-series,  math. 
                  models, 9 others.

              b)  Graduate:   Math.  methods  of physics, Fourier series, 
                  Integral  transforms, Functional analysis, mathematical 

          II.  Directed ten Ph.D. dissertations in analysis, two in statistics. 

          III. Served as departmental statistical consultant, 3 semesters. 

          IV.  Coordinator of applied mathematics and physics program, 1975-1984. 

          V.   Various University Committees including Faculty Senate (twice). 


          1.   National Science Foundation "Analog Encryption" (with G. Davida)  $120,000, 1985-1988. 

         2.    National Science Foundation "Models of multispecies fisheries" US-Mexico Cooperative Research $3,520, 1986-1989.

         3.    National   Science   Foundation   "Extension   of  sampling  theorems" (with Z. Nashed) $126,000, 1991-93.





          Gilbert G. Walter    

          Professor Emeritus of Mathematics 
          Department of Mathematical Sciences
          University of Wisconsin-Milwaukee 
          P.O. Box 413, Milwaukee, WI  53201 
                                                Telephone: (414)229-5528 
                                                Fax:  (414)229-4907 


          [1] Expansions of Distributions, Trans. A.M.S. (1965) 116,

          [2] Pointwise Convergence of Distribution Expansions, Studia
Math(1966) 26, 143-154. 

          [3] On Real Singularities of Legendre Expansions, Proc. A.M.S.
(1968) 19, 1407-1412. 

         [4] Singular Points and Hermite Series, Jour. of Math. Anal. 
 and Appl. (1969) 27, 495-500.

         [5] Legendre Series in Potential Scattering Theory, Analytic
Methods in Mathematical Physics, ed. R. R. Gilbert, (1970) 553-556. 

         [6] Series de Fourier-Tipos de Convergencias, Boletin Del
Departmento De Ciencias Uni. Cat. Peru. Ano. (1969) 11, No. 4, 40-53. 

         [7] Un Punto de Vista de la Mathematica Moderna en Estadistica,
(algunas applicationes de functiones generalizadas en Estadistica)Annales
Cientificos VII (1969) Lima, Peru. 173-181 (with A. Fujimori).

         [8] Fourier Series and Analytic Representation of Distributions. 
SIAM Review (1970) 12, 272-276. 

         [9] Local Boundary Behavior of Harmonic Functions, III. Jour. of
Math. (1970) 16, 491-501. 

         [10] Hermite Series Solutions of Differential Equations, Jour. of
Diff. Equations (1971) 10, 1-16. 

         [11] Singular Points of Sturm-Liouville Series.  SIAM J. Math.
Anal.  (1971) 2, 393-401. 

         [12] Mathematical Models for Estimating Changes in Fish
Populations with Applications to Green Bay, Proc. 14th Conf. Great Lakes
Res. (1971), 170-184 (with W. Hoagman). 

         [13] Delay-Differential Equation Models for Fisheries, J. Fish.
Res. Board Canada (1973) 30, 939-945. 

         [14] A Method for Estimating Year Class Strength from Abundance
Data with Applications to Green Bay, Lake Michigan, Trans. Amer. Fish.
Soc. (1975) 104, (with W. Hoagman). 

         [15] Hermite Series as Boundary Values, Trans. A.M.S. (1976) 218,

         [16] Graphical Methods for Estimating Parameters in Simple Models
of Fisheries, J. Fish. Res. Board Can. (1975) 32, 2163-2168. 

         [17] Non-equilibrium Regulation of Fisheries, ICNAF Res. Doc. No.
75/19/131.  Selected Papers No. 1 (1976) 129-140. 

         [18] Some Eigenfunction Methods for Computing Numerical Fourier
Transform, J.  Inst.  Math.  Appl.  (1976)  18, 279-293 (with D. Schultz). 

         [19] Properties of Hermite Series Estimation of Probability
Density, Ann. Stat.(1977) 5, 1258-1264. 

         [20] Estimation of Densities Using Delta-Sequences, Ann. Stat.
(1979) 7, 328-340 (with J. Blum). 

         [21] A Surplus Yield Model with Incorporates Recruitment with
Applications to a Stock of Mackerel, Jour. of Fish. Res. Bd. of Canada
(1978) 35, 229-234. 

         [22] Mean Square Estimation of the Prior Distribution, SANKHA
(1979) 41a, 95-108 (with T. O'Bryan). 

         [23] Limits of Lipschitz-Hankel Integrals, J. Inst. Math.
Applies.  (1979) 24, 237-254 (with N. Salamon). 

         [24] Compartmental Models, Digraphs, and Markov Chains,
Compartmental Analysis of Ecosystem Models, Matis, Patten and White, eds.
(1979) 295-310. 

         [25] A Compartmental Model of Georges Bank, Compartmental
Analysis of Ecosystem Models, Matis, Patten and White, eds. (1979) 29-42. 

         [26] A Class of Spectral Density Estimators, Ann. Inst. Statist.
Math. (1980) 52, 65-80. 

         [27] Stability and Structure of Compartmental Models of
Ecosystems, Math. Bio. (1980) 51, 1-11. 

         [28] Estimation of Multivariate Density Function Using
Delta-Sequences, Ann. Stat. (1981) 9, 347-355 (with V. Susarla). 

         [29] Orthogonal Series Estimators of the Prior Distribution,
SANKYA (1981) 43A, 228-245.

         [30] Surplus Yield Models of Fisheries.  Quantitative Population
Dynamics, Chapman and Gallucci, eds., (1981) 151-180.  Int. Co-op. 

         [31] Series of Orthogonal Polynomials as Bound. Values, Siam J.
Math. Ann. (1981) 12, 502-513 (with P. Nevai). 

         [32] Series of Orthogonal Polynomials as Hyperfunctions, Siam J.
Math. Ann. (1982) 13, 664-675 (with A. Zayed). 

         [33] Estimation of Prior Using Differential Equations. Coll.
Math. Janos Bolyai, (1982) Non-Parametric Stat. Inf., B. V. Gnedenko, M.
L. Puri, I. Vincze, Eds. North Holland, 32, 57-75 (with J. Blum and V.

         [34] Addendum to "Properties of Hermite Series Estimation of
Probability Density", Ann. Stat. (1980) 8, 454-455. 

         [35] Integral Equation Estimator of the Prior Distribution,
SANKYA (1984) 46A, 75- 84. 

         [36] Stability in Compartmental Models, Population Biology,
Freedman Stolobeck, Eds., Springer (1984) 372-378. 

         [37] A General Approach to Classification Problems, Info. Sci.
(1983) 30, 67-77.

         [38] Some Equivalent Compartmental Models, Math. Bio. (1983) 64,

         [39] Passage Time, Resilience, and Structure of Compartmental
Models, Math. Bio. (1983) 63, 199-213. 

         [40] A Fixed Point Theorem and its Application to a Central Limit
Theorem, Archiv. Mat. (1984) 43, 258-264 (with G. Hamedani). 

         [41] An Alternative Approach to Ill-posed Problems, J. Int. Equa.
and Appl. (1988) 1, 287-301. 

         [42] A Simple Solution to a Nonparametric MLE Problem, Ann. Stat.
(1984) 12, 372-379 (with J. R. Blum). 

          [43] Complexity of Compartmental Models, Math. Bio (1984) 70,

          [44] Eigenvalues and Structure of Comp. Models, Math. Bio.
(1984) 71, 181-199.

          [45] Complexity and Stability in Comp. Models, Siam J. Alg.
Disc. Meth. (1985) 6, 39-46.

         [46] On the Singularities of Singular S-L Expansions and an
Associated Class of Elliptic PDE's, SIAM J. Math. Anal. (1985) 16, 725-740
(with A. Zayed). 

         [47] Real Singularities of Singular S-L Expansions, SIAM J. Math.
Anal. (1987) 18, 219-227 (with A. Zayed). 

         [48] Orthogonal Polynomial Estimators of the Prior Distribution
of a Compound Poisson Distribution, SANKYA (1985) 47, 222-230. 

         [49] A Characterization of Reciprocal Random Variables, Pub.
Inst. Stat. Univ. (Paris) (1985) 30, 45-60 (with G. Hamedani). 

         [50] On the Product of Symmetric Random Variables, Stat. Prob.
Letters (1985) 3, 251-254 (with G. Hamedani). 

          [51] Complex Eigenvalues of Compartmental Models, Math. Bio.
(1985) 75, 143-157.

         [52] On Properties of Subindependent Random Variables, Bull.
Iran. Math. Soc. (1985) 11, 45-51 (with G. Hamedani). 

         [53] A Robust Approach to Equilibrium Yield Curves, Canadian J.
of Fisheries and Aquatic Sciences (1986) 43, 1332-1339. 

          [54] Size Identifiability of Compartmental Models, Math. Bio.
(1986) 81, 165-176. 

         [55] On the Singularities of Continuous Legendre Transforms,
Proc. AMS (1986) 97, 673-681 (with A. Zayed). 

         [56] A Public Key Analog Cryptosystem, Proc. of Eurocrypt (1987)
187, IV 23-26 (with G. Davida). 

         [57] A Class of Analog Cryptosystem, Proc. of Securicom '87
(1987) 215-223, SEDEP, Paris (with G. Davida). 

         [58] Empiric Bayes Estimation of Binomial Probability, Comm. 
               Statist. (1987) 16(2), 559-577 (with G. Hamedani). 

         [59] On Self-Reciprocal Random Variables, Pub.  Inst. Stat. Univ.
Paris (1987) 32, 45-66 (with G. Hamedani). 

         [60] The Continuous (,) Jacobi Transform and its Inverse when
               ++1 is a Positive Integer, Trans. AMS (1988) 305, 653-664
               (with A. Zayed). 

         [61] A Finite Continuous Gegenbauer Transform and its Inverse II,
SIAM J. on App. Math. (1988) 48, 680-688. 

         [62] Empiric Bayes Estimation of Hypergeometric Probability, in
METRIKA (1988) 35, 127-143 (with G. Hamedani). 

         [63] Bayes Estimation of the Binomial Parameter n, Comm. Statist.
(1988) 17, 1829-1843 (with G. Hamedani). 

         [64] Bayes-Empirical Bayes Estimation for Discrete Exponential
Families, Ann.  Inst.  Stat.  Math.  (1988)  41, 101-119 (with G.

         [65] Sampling Band Limited Functions of Polynomial Growth, SIAM
J. Math. Anal. (1988) 19, 1198-1203. 

         [66] Abel Summability for a Distribution Sampling Theorem, in
Generalized Functions and Convergence Structures (1988) 349-357,
Stankovic, Pap, Pilipovic, Viadimirov, eds., Plenum Press, New York. 

         [67] The Jacobi Transform and its Inverse, J. of Approx. Theory
(1991) 60, 83-100, (with T. Koornwinder). 

         [68] Recent Extensions of the Sampling Theorem, in Signal
Processing, Part I, Auslander, Kailath, & Mitter, eds. IMA Vol. Math &
Appl. #22 (1990) 229-238. 

         [69] Empirical Bayes Estimation of the Binomial Parameter n,
               Comm. Stat. (1990) 19, 2065-2084 (with G. Hamedani). 

         [70] Some Wavelet Sampling Theorems, Proceedings of 1990 ICSS
Conference, Princeton (1990) 660-664. 

         [71] A New Approach to Sampling Theorems for Signals in Sobolev
Spaces, Proc.  of 1990 ICSS Conference, Princeton (1990) 670-676 (with Z.

         [72] Remarks on Projection Pursuit Regression and Density
Estimation, Stoch. Anal. & Appl. (1992) 10, 213-222 (with L. Rejto). 

         [73] Bayes-Empirical Bayes Estimation for Natural Exponential
Families with Quadratic Variance Function, Annals Stat. (1991) 19,
1191-1224 (with G. Hamedani). 

         [74] General Sampling Theorems for Functions in Reproducing
Kernel Hilbert Spaces, Math. of Control, Systems, and Signals (1991) 4,
373-412 (with Z. Nashed). 

         [75] On the Inversion of Integral Transforms Associated with
Sturm-Liouville Problems, J. of Math Anal. & Appl. (1992) 164, 285-306
(with A. Zayed). 

          [76] Discrete Discrete Wavelets, SIAM J. Math. Anal. (1992) 23,

         [77] Wavelets Based on Orthogonal Basic Splines, J. Applicable
Anal. (1992) 47, 71-85 (with H. Volkmer). 

         [78] Approximation of the Delta Function by Wavelets, J. Approx. 
               Theory (1992) 71, 329-343. 

         [79] A Sampling Theorem for Wavelet Subspaces, IEEE Trans. Info. 
               Theory (1992) 38, 881-884. 

         [80] Non Uniform Sampling of Bandlimited Functions of Polynomial
Growth, SIAM J. Math. Anal. (1992) 23, 995-1003. 

         [81] Differential Operators which Commute with Characteristic
Functions with Applications to a Lucky Accident, J. Complex Var. (1992)
18, 7-12. 

         [82] Wavelets and Generalized Functions, in Wavelets a Tutorial;
Theory and Applications, C. Chui, ed. (1992) 51-70. 

         [83] Reconstruction of a Function from its Values on a Subset of
its Domain:  New Sampling Theorems,in Integral Equations and Inverse
Problems, Petkov and Lazarov, ed. Pitman Research Notes #235, 175-184
(1991) (with Z. Nashed).

         [84] Sampling Theorems as Part of Wavelet Theory, Proc. Conf. on
Info Science & Systems, Johns Hopkins (1991) 907-912. 

         [85] Sampling Locally Bandlimited Functions, Proc.  Conf.  on Inf
Science & Systems, Johns Hopkins (1991) 239-240. 

          [86] Negative Spline Wavelets, J. Math. Anal. Appl. (1993) 177,

         [87] Analytic Representations Using Wavelets, J. Complex
Variables (1994) 26, 235-244. 

         [88] A Note on Estimation of Generalized Densities, Comm. in
Stat. (1992) 7, 1807-1821 (with D. Cuevas). 

          [89] Wavelets:  A New Tool in Applied Mathematics, UMAP Journal
(1993) 142, 155-178.

         [90] Sampling Theorems and Wavelets, Handbook of Statistics, Vol.
10, N.K. Bose and C.R. Rao, eds. (1993) 883-903, Elsevier. 

          [91] Wavelets with an Oversampling Property, Indag. Mathem.
(1993) 4, 499-507.

          [92] Pointwise Convergence of Wavelet Expansion, J. Approx.
Theory (1995) 80, 108-118

         [93] A Wavelet-Based KL-Like Expansion for Wide Sense Stationary
Random Processes, IEEE Trans. Info. Th. (1994) 42, 1737-1745 (with J.

         [94] Wavelets Based on Band-Limited Processes with a K-L Type
Property, Proc.  SPIE Conf. Mathematical Imaging (1993) (with J. Zhang). 

         [95] Advantages and Disadvantages of Density Estimation with
Wavelets, Comp.  Sci.  Stat.  (1993)  24, 234-243 (with J.K.  Ghorai). 

         [96] Analytic Representation of Distributions Using Wavelets,
               in Generalized Functions and their applications, (1993) 
               281-291, Plenum, New York. 

         [97] Irregular Sampling in Wavelet Subspaces, J. Fourier Anal. &
Appl. (1995) 2, 181-189 (with Y. Liu). 

         [98] Wavelet Neural Networks for Function Learning, IEEE Trans.
Sig. Proc. (1995) 43 1485-1498 (with J. Zhang, Y. Miao, W. N. Lee). 

         [99] Discussion of Donoho, Et. Al, Wavelet Shrinkage: 
Asymptopia?  J. Royal Stat. Soc. (1995). 

         [100] Translation and dilation invariance in orthogonal wavelets,
App. Comput. Harmonic Anal. (1994) 1 344-349. 

         [101] Characterization of analytic functions in terms of their
wavelet coefficients, Complex Variables Th. & App. (1996) 29, 365-376
(with A. Zayed) 

         [102] Reproducing kernel Hilbert Spaces from sampling expansions,
in Mathematical Analysis, wavelets, and signal processing, Contemp. Math #
190 (1995) 221-226, AMS, Providence RI (with Z. Nashed) 
	 [103] Periodic Wavelets from Scratch, Comp Anal &
Appl 1(1999) 29-41(with L. Cai) 
	 [104] Gibbs Phenomenon for sampling series and what to do about
it, J Fourier Anal & Appl 4(1998)357-375 (with H-T Shim) 

	 [105] Positive Estimation with Wavelets, Cont. Math. 216 (1998)
63-79 (with X. Shen) 
	 [106] Orthonormal wavelets with simple closed form expressions,
 IEEE Trans on Sig. Proc. 46(1998) 2248-2251(with J.Zhang) 
	 [107] Approximation with impulse trains, Result.
Math, 34(1998) 185-196
	 [108] Sampling and Multiwavelets, Proc. of Sampta '97, Aveiro,
Portugal (1997) 313-316 (with L. Cai) 

	 [109] Multiresolution analysis with sampling subspaces, Frac. Calc
& Applied Anal 1 (1998) 109-124 (with A. Zayed) 
	[110] Deconvolution using Meyer wavelets, J. Integral Equations &
Appl. 11 (1999) 515-534 (with X. Shen)

	[111] Continuous Non-negative wavelets and their use in density
estimation, Statist.-Theory and Methods,28 (1999) 1-17 ( with

	[112] Density estimation in the presence of noise, Stat. & Prob.
letters, 41 (1998) 237-246

	[113] A Class of bandlimited cardinal Wavelets, Advances in
Mathematics, 26 (1997), 523-528 (with Youming Liu)

	[114] A substitute for summability in wavelet exapansions, in
Analysis of Divergence, W. Bray and C. Stanojevic, eds.(1999) 51-63,
Birkhauser, Boston (with X. Shen)

	[115] Green' function based wavelets, IEEE-UFFC Conf Proc.
2000, (with A.R. Baghai-Wadji)

	[116] Wavelets in closed form, in Wavelet Transforms and
Time-Frequency Analysis, L. Debnath, ed.(2001) 121-143, Birkhauser,
Boston (with A. Zayed)

	[117] Wavelets and Sampling, in Modern Sampling Theory, J.
Benedetto and P. Ferreira, eds. (2001) 49-71, Birkhauser, Boston

	[118] A general approach to Gibbs phenomenon, 
J. Complex Variables 47(2002) 731-743

	[119] Positive Sampling in wavelet subspaces, Applied
and Comp. Harmonic Analysis 12, (2002) 150-165 (with X. Shen)

	[120] Meyer wavelet regularization, J. Numer. Fncl. 
Anal & Optimization 23(1&2), (2002) 195-215 (with X. Shen)

	[121] Compartmental Models, in Encyclopedia of Nonlinear 
Science, ed. Alwyn Scott, (2004) Routledge,.New York and London. 

	[122] Sampling with Prolate Spheroidal Wave Functions, 
J. Sampling Th. in Sig. Image Proc. 2(2003) 25-52 (with X. Shen)

	[123] Wavelets based on Prolate Spheroidal Wave Functions, 
J. Fourier Anal. & Appl. 10(2004) 1-25 (with X. Shen)

	[124] A Sampling Expansion for non Bandlimited Signals in 
Chromatic Derivatives, IEEE Trans. Sig Proc. 53(2005) 1291-1298 
(with X. Shen)

	[125] The raised-cosine wavelet in computerized tomography, 
Applicable Analysis, 83(2004) 199-215 (with T. Soleski)

	[126] Prolate spheroidal wavelets: translation, convolution, 
and differentiation made easy, J. Fourier Anal. Appl. 11(2005) 73-84.

	[127] Prolate spheroidal wavelet sampling in computerized 
tomography, J. Sampling Th. in Sig. Image Proc. (2005).(with T. Soleski)

	[128] Wavelet like behavior of Slepian functions and their 
use in density estimation, Comm. Stat., Th. and Methods 34(2005) 687-711
(with X. Shen)

	[129] A new friendly method of computing prolate spheroidal 
wave functions and wavelets, Comp. Harmonic Anal. 19(2005) 432-443
(with T. Soleski). 

	[130] Periodic prolate spheroidal wavelets, to appear in 
Num. Funct. Anal. Optim. 26(2005) (with X. Shen) 

	[131] Prolate spheroidal wave functions and wavelets, 
to appear in Advances in Imaging and Electron Physics, 
P. W. Hawkes , ed. Elsevier (2005)

	[132] Prolate spheroidal wavelets in higher dimensions, 
to appear in J. Int. Equa. and Appl. (2006)


        [1]  Wavelets  and  Other  Orthogonal  Systems  with
Applications, CRC Press, Boca Raton, FL, 248 p. (1994). 

Now translated into Japanese under title: 
"Wevuretto to Chokkokansukei" by 
 S. Sakakibara, T. Mandai, and R. Ashino, 
Tokyo Denki University Press, Tokyo, 307 p.(2001).

	[2] Compartmental Modeling with Networks, Birkhauser, Boston,   
250 p. (1999) (with M. Contreras)

	[3] New, fatter, improved, more expensive edition of [1],
Wavelets and Other Orthogonal Systems, Chapman & Hall/CRC, Boca Raton, 370
p. (2001) (with X. Shen)