Harmonic, wavelet and p-adic analysis PDF
Preview Harmonic, wavelet and p-adic analysis
HARMONIC, WAVELET AND p-ADIC ANALYSIS EDITORIAL BOARD Nguyh Minh Chuang Youri V. Egorov Takeyuki Hida Andrei Khrennikov Yves Meyer David Mumford Roger Temam Nguygn Minh Tri Vii Kim Tudn HARMONIC, WAVELET AND p-ADIC ANALYSIS editors N M Choung A Khrennikov Institute of Mathematics, Vietnamese-Acad. of Sci. & Tech., Vietnam Y Meyer ENS-Cachan, France Yu V Egorov University of Toulouse, France D Mumford Brown University, USA World Scientific NEW JERSEY . LONDON . SINGAPORE . BEIJING . SHANGHAI . HONG KONG . TAIPEI . CHENNAI Published by World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore 596224 USA ofice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK ofice: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-PublicationD ata A catalogue record for this book is available from the British Library. HARMONIC, WAVELET AND p-ADIC ANALYSIS Copyright Q 2007 by World Scientific Publishing Co. Re. Ltd. All rights reserved. This book, or parts thereoj may not be reproduced in any form or by any means, electronic or mechanical, includingphotocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-I 3 978-981-270-549-5 ISBN-I0 981-270-549-X Printed in Singapore by B & JO Enterprise V PREFACE The mutual influence between mathematics, sciences and technology is more and more widespread. It is both important and interesting to discover more and more profound connections among different areas of Mathematics, Sciences and Technology. Particularly exciting has been the discover in recent years of many relations between harmonic analysis, wavelet analysis and padic analysis. So in 2005, from June 10 to 15, at the Quy Nhon University of Vietnam, an International Summer School on "Harmonic, wavelet and padic analy- sis" was organized in order to invite a number of well known specialists on these fields from many countries to give Lectures to teachers, researchers, and graduate students Vietnamese as well as from foreign institutions. This volume contains the Lectures given by those invited Professors, including some from Professors who could not come to the School. These Lectures are concerned with deterministic as well as stochastic aspects of the subjects. The contents of the book are divided in two Parts and four Sections. Part A deals with wavelets and harmonic analysis. In Section I some mathematical methods, especially wavelet theory, one of the most powerful tools for solution of actual problems of mathematical physics and engineer- ing, are introduced. The connection between wavelet theory and time op- erators of statistical mechanics is established. Wavelets are also connected to the theory of stochastic processes. Multiwavelet and multiscale approxi- mations and localization operator methods are presented. Section I1 is devoted to some of the most interesting aspects of harmonic analysis. The nonlinear spectra based on the so called Fiber spectral anal- ysis with applications are discussed. Here the very famous critical Sobolev problem is developed, too. The representation theory of affine Hecke al- gebras, the quantized algebras of functions on affine Hecke algebras are reviewed and the so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representation are classified. A survey is made of the past 40 years of the Andreotti-Grauert legacy as well as its recent de- vi Preface velopments (cohomologically q-convex, cohomologically q-complete spaces, strong q-pseudoconvexity, pseudoconvexity of order m) with some new re- sults which did not appear elsewhere. In Part B some recent developments in deterministic and stochastic analysis over archimedean and non-archimedean fields are introduced. In Section I11 some Cauchy pseudodifferential problems over padic fields, some classes of padic Hilbert transformations in some classes of padic spaces, say BMO, VMO, are investigated. An analogue of probability theory for probabilities taking values in topological groups is developed. A review is presented of non-Kolmogorovian models with negative, complex, and padic probabilities with some applications in physics and cognitive sciences. Section IV is devoted to archimedean stochastic analysis, more precisely to some recent aspects on stochastic integral equations of Fredholm type, on reflecting stochastic differential equations with jumps, on analytic processes and Levy processes. Here an interesting relation between harmonic analysis, group theory and white noise theory is also developed. The Editors vii CONTENTS Preface V Part A Wavelet and Harmonic Analysis Chapter I Wavelet and Expectations $1.W avelets and Expectations: A Different Path to Wavelets 5 Karl Gustafson $2. Construction of Univariate and Bivariate Exponential Splines 23 Xiaoyan Liu 53. Multiwavelets: Some Approximation-Theoretic Properties, Sampling on the Interval, and Translation Invariance 37 Peter R. Massopust $4.M ulti-Scale Approximation Schemes in Electronic Structure Calculation 59 Reinhold Schneider and Toralf Weber 55. Localization Operators and Time-Frequency Analysis 83 Elena Cordero, Karlheinz Grochenig and Luigi Rodino Chapter I1 Harmonic Analysis 56. On Multiple Solutions for Elliptic Boundary Value Problem with Two Critical Exponents 113 Yu. V. Egorov and Yavdat Il’yasov ... viii Contents $7. On Calculation of the Bifurcations by the Fibering Approach 141 Yavdat I1 'yasov $8. On a Free Boundary Transmission Problem for Nonhomogeneous Fluids 157 Bu.i An Ton 59. Sampling in Paley-Wiener and Hardy Spaces 175 Vu Kim Tuan and Amin Boumenir $10. Quantized Algebras of Functions on Affine Hecke Algebras 211 Do Ngoc Diep $11. On the C-Analytic Geometry of q-Convex Spaces 229 Vo Van Tan Part B P-adic and Stochastic Analysis Chapter I11 Over padic Field 512. Harmonic Analysis over padic Field I. Some Equations and Singular Integral Operators 271 Nguyen Manh Chuong, Nguyen Van Co and Le Quang Thuan $13. p-adic and Group Valued Probabilities 29 1 Andrei Khrennikov Chapter IV Archimedean Stochastic Analysis $14. Infinite Dimensional Harmonic Analysis from the Viewpoint of White Noise Theory 313 Takeyuki Hida $15. Stochastic Integral Equations of Fredholm Type 331 Shigeyoshi Ogawa Contents ix $16. BSDEs with Jumps and with Quadratic Growth Coefficients and Optimal Consumption 343 Situ Rong $17. Insider Problems for Markets Driven by LBvy Processes 363 Arturo Kohatsu-Hzga and Makato Yamazato
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