Interpolation of Linear Operators
Author : S. G. Krein
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 10,67 MB
Release : 2002-10-21
Category : Mathematics
ISBN : 0821831763
Author : S. G. Krein
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 10,67 MB
Release : 2002-10-21
Category : Mathematics
ISBN : 0821831763
Author : I. Gohberg
Publisher : Birkhäuser
Page : 311 pages
File Size : 21,77 MB
Release : 2013-11-11
Category : Science
ISBN : 3034877013
Author : I. Gohberg
Publisher : Birkhäuser
Page : 305 pages
File Size : 44,60 MB
Release : 1990-10-01
Category : Science
ISBN : 9783764325305
The classicallossless inverse scattering (LIS) problem of network theory is to find all possible representations of a given Schur function s(z) (i. e. , a function which is analytic and contractive in the open unit disc D) in terms of an appropriately restricted class of linear fractional transformations. These linear fractional transformations corre spond to lossless, causal, time-invariant two port networks and from this point of view, s(z) may be interpreted as the input transfer function of such a network with a suitable load. More precisely, the sought for representation is of the form s(Z) = -{ -A(Z)SL(Z) + B(z)}{ -C(Z)SL(Z) + D(z)} -1 , (1. 1) where "the load" SL(Z) is again a Schur function and _ [A(Z) B(Z)] 0( ) (1. 2) Z - C(z) D(z) is a 2 x 2 J inner function with respect to the signature matrix This means that 0 is meromorphic in D and 0(z)* J0(z) ::5 J (1. 3) for every point zED at which 0 is analytic with equality at almost every point on the boundary Izi = 1. A more general formulation starts with an admissible matrix valued function X(z) = [a(z) b(z)] which is one with entries a(z) and b(z) which are analytic and bounded in D and in addition are subject to the constraint that, for every n, the n x n matrix with ij entry equal to X(Zi)J X(Zj )* i,j=l, . . .
Author : Ronald A. DeVore
Publisher :
Page : 25 pages
File Size : 45,5 MB
Release : 1978
Category :
ISBN :
Author : Colin Bennett
Publisher : Academic Press
Page : 489 pages
File Size : 39,83 MB
Release : 1988-04-01
Category : Mathematics
ISBN : 0080874487
This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.
Author :
Publisher :
Page : 92 pages
File Size : 23,39 MB
Release : 2008
Category :
ISBN :
Author : I. Gohberg
Publisher : Birkhäuser
Page : 308 pages
File Size : 50,56 MB
Release : 2012-12-06
Category : Science
ISBN : 3034886152
Author : Albrecht Pietsch
Publisher : Springer Science & Business Media
Page : 877 pages
File Size : 14,64 MB
Release : 2007-12-31
Category : Mathematics
ISBN : 0817645969
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Author : Traian Ceauşu
Publisher :
Page : 18 pages
File Size : 37,58 MB
Release : 1981
Category :
ISBN :
Author : Hari Bercovic
Publisher : Birkhäuser
Page : 311 pages
File Size : 20,76 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034884222
A collection of articles emphasizing modern interpolation theory, a topic which has seen much progress in recent years. These ideas and problems in operator theory, often arising from systems and control theories, bring the reader to the forefront of current research in this area.