A.V. Kuzhel and S.A. Kuzhel
Regular Extensions of Hermitian Operators
The concept of regular extensions of an Hermitian (non-densely defined) operator was introduced by A. Kuzhel in 1980. This concept is a natural generalization of proper extensions of symmetric (densely defined) operators. The use of regular extensions enables one to study various classes of extensions of Hermitian operators without using the method of linear relations. The central question in this monograph is to what extent the Hermitian part of a linear operator determines its properties. Various properties are investigated and some applications of the theory are given.
Chapter 1 deals with some results from operator theory and the theory of extensions. Chapter 2 is devoted to the investigation of regular extensions of Hermitian (symmetric) operators with certain restrictions. In chapter 3 regular extensions of Hermitian operators with the use of boundary-value spaces are investigated. In the final chapter, the results from chapters 1-3 are applied to the investigation of quasi-differential operators and models of zero-range potential with internal structure.
This book will be of value and interest to researchers working in the field of operator theory and applications.
1998; xii+274 pages
ISBN 90-6764-294-0
Editor: M.L. Puri
Asymptotics in Statistics and Probability
Papers in Honor of George Gregory Roussas
Contents:
Preface
Contributors
George Gregory Roussas: Biographical Sketch
REACT Trend Estimation in Correlated Noise
Rudolf Beran
Higher Order Analysis at Lebesgue Points
A. Berlinet and S. Levallois
Regression Analysis for Multivariate Failure Time Observations
T. Cai and L.J. Wei
Local Estimation of a Biometric Function with Covariate Effects
Zongwu Cai and Lianfen Qian
The Estimation of Conditional Densities
X. Chen, O. Linton and P.M. Robinson
Functional Limit Theorems for Induced Order Statistics of a Sample from a Domain of Attraction of -Stable Law, (0,2)
Yu. Davydov and V. Egorov
Limit Laws for Kernel Density Estimators for Kernels with Unbounded Supports
Paul Deheuvels
Inequalities for a New Data-Based Method for Selecting Nonparametric Density Estimates
Luc Devroye, Gabor Lugosi and Frederic Udina
?'102-Fuzzy Stochastics
C.A. Drossos, G. Markakis and P.L. Theodoropoulos
Detecting Jumps in Nonparametric Regression
Ch. Dubowik and U. Stadtm・ler
Some Recent Results on Inference Based on Spacing
Kaushik Ghosh and S. Rao Jammalamadaka
Extending Correlation and Regression from Multivariate to Functional Data
G. He, H.G. M・ler and J.L. Wang
2000; xiv+430 pages
ISBN 90-6764-333-5
Yu.E. Anikonov
Inverse Problems for Kinetic and Other Evolution Equations
Inverse and Ill-Posed Problems Series
This monograph in the Inverse and Ill-Posed Problems Series deals with methods of studying multidimensional inverse problems for kinetic and other evolution equations, in particular transfer equations. The methods used are applied to concrete inverse problems, especially multidimensional inverse problems applicable in
linear and nonlinear statements.
A significant part of the book contains formulas and relations for solving inverse problems, including formulas for the solution and coefficients of kinetic equations, differential-difference equations, nonlinear evolution equations, and second order equations.
This monograph will be of value and interest to mathematicians, engineers and other specialists dealing with inverse and ill-posed problems.
2001; viii+270 pages
ISBN 90-6764-345-9
A.S. Blagoveshchenskii
Inverse Problems of Wave Processes
Inverse and Ill-Posed Problems Series
This volume in the Inverse and Ill-Posed Problems Series studies dynamical inverse problems, i.e. such problems whose data are the values of wave fields.
The monograph deals with the problem of determination of one or more coefficients of a hyperbolic equation or a system of hyperbolic equations. The desired coefficients are functions of point. Most attention is given to the case where the required functions depend only on one coordinate. The first chapter of the book
deals mainly with methods of solution of one-dimensional inverse problems. The second chapter focuses on scalar inverse problems of wave propagation in a layered medium. In the final chapter inverse problems for elasticity equations in stratified media and acoustic equations for moving media are given.
This monograph will be of value and interest to researchers in the fields of mathematical physics, geophysics, acoustics, elasticity theory, and electrodynamics.
2001; viii+138 pages
ISBN 90-6764-344-0
V.D. Liseikin
Layer Resolving Grids and Transformations for Singular
Perturbation Problems
The approach of layer-damping coordinate transformations to treat singularly perturbed equations is a relatively new, and fast growing area in the field of applied mathematics. This monograph aims to present a clear, concise, and easily understandable description of the qualitative properties of solutions to singularly perturbed problems as well as of the essential elements, methods and codes of the technology adjusted to numerical solutions of equations with singularities by applying layer-damping coordinate transformations and corresponding layer-resolving grids.
The first part of the book deals with an analytical study of estimates of the solutions and their derivatives in layers of singularities as well as suitable techniques for obtaining results. In the second part, a technique for building the coordinate transformations eliminating boundary and interior layers, is presented. Numerical
algorithms based on the technique which is developed for generating layer-damping coordinate transformations and their corresponding layer-resolving meshes are presented in the final part of this volume.
This book will be of value and interest to researchers in computational and applied mathematics.
2001; xiv+284 pages
ISBN 90-6764-346-7
S.M. Prigarin
Spectral Models of Random Fields in Monte Carlo Methods
Spectral models were developed in the 1970s and have appeared to be very promising for various applications. Nowadays, spectral models are extensively used for stochastic simulation in atmosphere and ocean optics, turbulence theory, analysis of pollution transport for porous media, astrophysics, and other fields of science.
The spectral models presented in this monograph represent a new class of numerical methods aimed at simulation of random processes and fields. The book is divided into four chapters, which deal with scalar spectral models and some of their applications, vector-valued spectral models, convergence of spectral models, and problems of optimisation and convergence for functional Monte Carlo methods. In addition, the monograph includes four appendices, in which auxiliary information is presented and additional problems are discussed.
The book will be of value and interest to experts in Monte Carlo methods, as well as to those interested in the theory and applications of stochastic simulation.
2001; xii+198 pages
ISBN 90-6764-343-2
S.P. Shishatskii, A. Asanov and E.R. Atamanov
Uniqueness Problems for Degenerating Equations and Nonclassical Problems
Inverse and Ill-Posed Problems Series
The study of Cauchy problems for degenerating equations and systems is a wide and actively developing area. However, the majority deals mainly with Cauchy problems for hyperbolic equations and systems and characteristic Cauchy problems for parabolic equations and systems.
This volume in the Inverse and Ill-Posed Problems Series presents the results that were obtained on uniqueness for the main (ill-posed in the regular case) Cauchy problems for equations of the second order with exponential degeneracy. The Cauchy problem for a degenerating elliptic equation, the noncharacteristic Cauchy problem, and the mixed problem with reversed time for a degenerating parabolic equation are considered. Stability estimates that guarantee conditional well-posedness of the considered Cauchy problems in terms of the inverse problems theory are given, along with uniqueness theorems.
2001; xii+178 pages
ISBN 90-6764-341-6