Best Poisson Approximation of Poisson Mixtures. A Linear Operator Approach -- On Some Classes of Diffusion Equations and Related Approximation Problems -- Recent Developments in Barycentric Rational Interpolation -- Approximation on Simplices and Orthogonal Polynomials -- (0, 2) Pál-type Interpolation: A General Method for Regularity -- Sufficient Convergence Conditions for Certain Accelerated…
Mizan Rahman, His Mathematics and Literary Writings -- On the Completeness of Sets of q-Bessel Functions J?(3)(x; q) -- a-Gaussian Polynomials and Finite Rogers-Ramanujan Identities -- On a Generalized Gamma Convolution Related to the q-Calculus -- Ramanujan and Cranks -- The Saalschütz Chain Reactions and Multiple q-Series Transformations -- Painlevé Equations and Associated Polynomials -- Z…
Semyon Yakovlevich Khavinson (May 17, 1927 – January 30, 2003) -- S.Ya. Khavinson: Bibliography -- S.Ya. Khavinson: Photos -- The Structural Formulae for Extremal Functions in Hardy Classes on Finite Riemann Surfaces -- Extremal Problems for Nonvanishing Functions in Bergman Spaces -- Generalization of Carathéodory’s Inequality and the Bohr Radius for Multidimensional Power Series -- Remar…
Inverse Scattering with Rational Scattering Coefficients and Wave Propagation in Nonhomogeneous Media -- Aluthge Transforms and the Convex Hull of the Spectrum of a Hilbert Space Operator -- Maximal Nevanlinna-Pick Interpolation for Points in the Open Unit Disc -- On the Numerical Solution of a Nonlinear Integral Equation of Prandtl’s Type -- Fourier Integral Operators and Gelfand-Shilov Spac…
Operators on Sequences -- Basic Rank Selectors, Pulses and Impulses -- LULU-Smoothers, Signals and Ambiguity -- LULU-Intervals, Noise and Co-idempotence -- Smoothing and Approximation with Signals -- Variation Reduction and Shape Preservation -- Multiresolution Analysis of Sequences -- The Discrete Pulse Transform -- Fair Comparison with Linear Smoothers -- Interpretation and Future.This monogr…
Global Smoothness Preservation, Univariate Case -- Partial Shape Preservation, Univariate Case -- Global Smoothness Preservation, Bivariate Case -- Partial Shape Preservation, Bivariate Case.This monograph examines and develops the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP) in the field of interpolation of functions. The study is developed for the u…
Overview and Basic Facts -- Gaussian Processes and Related Structures -- Matching Theorems -- The Bernoulli Conjecture -- Families of distances -- Applications to Banach Space Theory.Author's Note: The material of this book has been reworked and expanded with a lot more detail and published in the author's 2014 book "Upper and Lower Bounds for Stochastic Processes" (Ergebnisse Vol. 60, ISBN 978…
Basic Matrix Theory and Linear Algebra -- Multivariate Distributions -- Distribution Expansions -- Multivariate Linear Models.The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The b…
1 Approximation with Polynomials -- 1.1 Approximation of a function on an interval -- 1.2 Weierstrass’ theorem -- 1.3 Taylor’s theorem -- 1.4 Exercises -- 2 Infinite Series -- 2.1 Infinite series of numbers -- 2.2 Estimating the sum of an infinite series -- 2.3 Geometric series -- 2.4 Power series -- 2.5 General infinite sums of functions -- 2.6 Uniform convergence -- 2.7 Signal transmissio…