Umfang:
1 online resource (xix, 619 pages)
ISBN:
9781107027787
,
9781139226769
Serie:
New mathematical monographs 21
Inhalt:
An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
Inhalt:
Machine generated contents note: List of figures; Preface; List of symbols; Important conventions; 1. *Normed linear spaces and their operators; 2. Some families of operators; 3. Harmonic functions on the open unit disc; 4. Analytic functions on the open unit disc; 5. The corona problem; 6. Extreme and exposed points; 7. More advanced results in operator theory; 8. The shift operator; 9. Analytic reproducing kernel Hilbert spaces; 10. Bases in Banach spaces; 11. Hankel operators; 12. Toeplitz operators; 13. Cauchy transform and Clark measures; 14. Model subspaces KT; 15. Bases of reproducing kernels and interpolation; Bibliography; Index
Anmerkung:
Title from publisher's bibliographic system (viewed on 27 Oct 2016)
Weitere Ausg.:
ISBN 9781107027787
Weitere Ausg.:
The theory of H(b) spaces ; Volume 2 Cambridge, UK : Cambridge University Press, 2016 ISBN 9781107027787
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 9781107027787
Sprache:
Englisch
Schlagwort(e):
Hilbert-Raum
;
Hardy-Raum
;
Analytische Funktion
;
Linearer Operator
DOI:
10.1017/CBO9781139226769
Bookmarklink
