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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 expansions, 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 Theory. 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,

(withT. Soleski)

[130] Periodic Prolate Spheroidal Wavelets, Num. Funct.

Anal. Optim., 26(2005),. 953-976, (with X. Shen),

[131] Prolate Spheroidal Wave Functions and Wavelets,

in Advances in Imaging and Electron Physics, ed. P. W. Hawkes ,

pp. 225-295, Elsevier, 2006

[132] Prolate Spheroidal Wavelets in Higher Dimensions,

J. Integral Equa Appl., 18(2006), 415-435,

[133] Error Estimates for the PSWF Method in MRI, Adv. Math.,

19 pp. AMS, 2007 (to appear) (with T. Soleski)

[134] Gibbs Phenomenon in Higher Dimensions,

J. Fourier Anal. Appl., vol. 13, 2007 (to appear)

(with H-T. Shim, H. Volkmer)

[135], Construction of Periodic Prolate Spheroidal Wavelets

using Interpolation, Num. Funct. Anal. Optim., vol. 28, 2007

(to appear) (with X. Shen)

[136] Chromatic Series with Prolate Spheroidal Wave Functions,

J. Integral Equa Appl., 19(2007), (to appear)

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)

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