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 email: ggw@uwm.edu Biography: 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 recently. 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 Employment: 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- Davis 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 statistics. 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). Grants: 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. PUBLICATIONS:PUBLICATIONS of Gilbert G. Walter Professor Emeritus of Mathematics Department of Mathematical Sciences University of Wisconsin-Milwaukee P.O. Box 413, Milwaukee, WI 53201 USA Telephone: (414)229-5528 Fax: (414)229-4907 email: ggw@uwm.edu ARTICLES: [1] Expansions of Distributions, Trans. A.M.S. (1965) 116, 492-510. [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, 155-171. [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. Susarla). [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, 273-293. [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, 147-159. [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 (à,á) Jacobi Transform and its Inverse when à+á+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. Hamedani). [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. Nashed). [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, 1004-1014. [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, 239-253. [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. Zhang). [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, Commun.in Statist.-Theory and Methods,28 (1999) 1-17 ( with X.Shen) [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) BOOKS: [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)