Linear Spaces and Approximation / Lineare Räume und Approximation

Linear Spaces and Approximation / Lineare Räume und Approximation
Author: Butzer
Publisher: Birkhäuser
Total Pages: 641
Release: 2013-03-08
Genre: Science
ISBN: 3034871805
GET BOOK

The publication of Oberwolfach conference books was initiated by Birkhauser Publishers in 1964 with the proceedings of the conference 'On Approximation Theory', conducted by P. L. Butzer (Aachen) and J. Korevaar (Amsterdam). Since that auspicious beginning, others of the Oberwolfach proceedings have appeared in Birkhauser's ISNM series. The present volume is the fifth * edited at Aachen in collaboration with an external institution. It once again ad dresses itself to the most recent results on approximation and operator theory, and includes 47 of the 48 lectures presented at Oberwolfach, as well as five articles subsequently submitted by V. A. Baskakov (Moscow), H. Esser (Aachen), G. Lumer (Mons), E. L. Stark (Aachen) and P. M. Tamrazov (Kiev). In addition, there is a section devoted to new and unsolved problems, based upon two special problem sessions augmented by later communications from the participants. Corresponding to the nature of the conference, the aim of the organizers was to solicit both specialized and survey papers, ranging in the broad area of classical and functional analysis, from approximation and interpolation theory to Fourier and harmonic analysis, and to the theory of function spaces and operators. The papers were supplemented by lectures on fields represented for the first time in our series of Oberwolfach Conferences, so for example, complex function theory or probability and sampling theory.

Abstract Spaces and Approximation / Abstrakte Räume und Approximation

Abstract Spaces and Approximation / Abstrakte Räume und Approximation
Author: Butzer
Publisher: Birkhäuser
Total Pages: 417
Release: 2013-11-21
Genre: Science
ISBN: 3034858698
GET BOOK

The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily arbitrary to some extent. The Proceedings are dedicated to the memory of Jean Favard. It was Favard who gave the Oberwolfach Conference of 1963 a special impetus and whose absence was deeply regretted this time. An appreciation of his li fe and contributions was presented verbally by Georges Alexits, while the written version bears the signa tures of both Alexits and Marc Zamansky. Our particular thanks are due to E.

Best Approximation in Inner Product Spaces

Best Approximation in Inner Product Spaces
Author: Frank Deutsch
Publisher: Springer Science & Business Media
Total Pages: 368
Release: 2001-04-20
Genre: Computers
ISBN: 9780387951560
GET BOOK

This book evolved from notes originally developed for a graduate course, "Best Approximation in Normed Linear Spaces," that I began giving at Penn State Uni versity more than 25 years ago. It soon became evident. that many of the students who wanted to take the course (including engineers, computer scientists, and statis ticians, as well as mathematicians) did not have the necessary prerequisites such as a working knowledge of Lp-spaces and some basic functional analysis. (Today such material is typically contained in the first-year graduate course in analysis. ) To accommodate these students, I usually ended up spending nearly half the course on these prerequisites, and the last half was devoted to the "best approximation" part. I did this a few times and determined that it was not satisfactory: Too much time was being spent on the presumed prerequisites. To be able to devote most of the course to "best approximation," I decided to concentrate on the simplest of the normed linear spaces-the inner product spaces-since the theory in inner product spaces can be taught from first principles in much less time, and also since one can give a convincing argument that inner product spaces are the most important of all the normed linear spaces anyway. The success of this approach turned out to be even better than I had originally anticipated: One can develop a fairly complete theory of best approximation in inner product spaces from first principles, and such was my purpose in writing this book.

Nonlinear Functional Analysis and its Applications

Nonlinear Functional Analysis and its Applications
Author: E. Zeidler
Publisher: Springer Science & Business Media
Total Pages: 675
Release: 2013-12-11
Genre: Science
ISBN: 146125020X
GET BOOK

As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? ( y) What typical applications are there? Vll Preface viii Special emphasis is placed on motivation.

BULLETIN TOME XCI

BULLETIN TOME XCI
Author:
Publisher: Srpska akademija nauka i umetnosti
Total Pages: 50
Release: 1986-05-13
Genre:
ISBN:
GET BOOK

TABLE DES MATIERES 1. S. Aljaneie — Generalization of a Theorem due to Cesare, 1 2. M. D. Leko — A Class of Stationary Metrics and the case of Static Metrics of Space-time which gives Conics as 3-paths of Inertial Motions of Mass Points . 5 3. Z. A. Ivkovie — Non-linear Time-domain Analysis of Gaussian Process, General Case 13 4. M. Janc — Optimal and Suboptimal Solutions of a Simultaneous Approximation Problem 17 5. M. Janc — Nonlinear Approximation in Locally Convex Spaces 25 6. D. Stolle i D. Durovie — The 75-day Variation of the Geomagnetic Field and Solar Activity 33