Physical description 
1 online resource (207 p.) 
Notes 
Description based upon print version of record. 
Contents 
Preface; Contents; 1. Introduction; 1.1 Preliminary notions and notations; 1.1.1 Infinite matrices; 1.1.2 Analytic functions on disk; 1.1.3 Miscellaneous; 1.1.4 The Bergman metric; Notes; 2. Integral operators in infinite matrix theory; 2.1 Periodical integral operators; 2.2 Nonperiodical integral operators; 2.3 Some applications of integral operators in the classical theory of infinite matrices; 2.3.1 The characterization of Toeplitz matrices; 2.3.2 The characterization of Hankel matrices; 2.3.3 The main triangle projection; 2.3.4 B( 2) is a Banach algebra under the Schur product; Notes 

3. Matrix versions of spaces of periodical functions3.1 Preliminaries; 3.2 Some properties of the space C( 2); 3.3 Another characterization of the space C( 2) and related results; 3.4 A matrix version for functions of bounded variation; 3.5 Approximation of infinite matrices by matriceal Haar polynomials; 3.5.1 Introduction; 3.5.2 About the space ms; 3.5.3 Extension of Haar's theorem; 3.6 Lipschitz spaces of matrices; a characterization; Notes; 4. Matrix versions of Hardy spaces; 4.1 First properties of matriceal Hardy space; 4.2 HardySchatten spaces 

4.3 An analogue of the Hardy inequality in T14.4 The Hardy inequality for matrixvalued analytic functions; 4.4.1 Vectorvalued Hardy spaces HpX; 4.4.2 (Hp − q)multipliers and induced operators forvectorvalued functions; 4.5 A characterization of the space T1; 4.6 An extension of Shields's inequality; Notes; 5. The matrix version of BMOA; 5.1 First properties of BMOA( 2) space; 5.2 Another matrix version of BMO and matriceal Hankel operators; 5.3 Nuclear Hankel operators and the space M1,2; Notes; 6. Matrix version of Bergman spaces; 6.1 Schatten class version of Bergman spaces 

6.2 Some inequalities in BergmanSchatten classes6.3 A characterization of the BergmanSchatten space; 6.4 Usual multipliers in BergmanSchatten spaces; Notes; 7. A matrix version of Bloch spaces; 7.1 Elementary properties of Bloch matrices; 7.2 Matrix version of little Bloch space; Notes; 8. Schur multipliers on analytic matrix spaces; Notes; Bibliography; Index 
Summary 
This book gives a unified approach to the theory concerning a new matrix version of classical harmonic analysis. Most results in the book have their analogues as classical or newer results in harmonic analysis. It can be used as a source for further research in many areas related to infinite matrices. In particular, it could be a perfect starting point for students looking for new directions to write their PhD thesis as well as for experienced researchers in analysis looking for new problems with great potential to be very useful both in pure and applied mathematics where classical analysis has been used, for example, in signal processing and image analysis. 
Other author 
Ebook Library


Popa, Nicolae.

Subject 
Algebraic spaces. 

Matrices. 

Schur multiplier. 

Electronic books. 
ISBN 
9789814546782 94.00 (NL) 
