The method of orbits in interpolation theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chur [u.a.]
Harwood
1984
|
| Schriftenreihe: | Mathematical reports
1,2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX S., S. 349 - 515 |
Internformat
MARC
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| 100 | 1 | |a Ovčinnikov, V. I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The method of orbits in interpolation theory |c V. I. Ovchinnikov |
| 264 | 1 | |a Chur [u.a.] |b Harwood |c 1984 | |
| 300 | |a IX S., S. 349 - 515 | ||
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Datensatz im Suchindex
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| adam_text | Contents
Editor s Introduction ix
Introduction 349
§1 Banach couples
1.1 Definition of a Banach couple 355
1.2 Examples of Banach couples 357
1.3 Thesumandthe intersection of the spaces
of a couple 360
1.4 Mappings of Banach couples 361
1.5 Ideals of maps of Banach couples 364
1.6 Orbits of elements. Orbits, and coorbits
of spaces 368
1.7 Interpolation functors. The characteristic
function of an interpolation functor 370
1.8 Examples of interpolation functors 372
§2 Duality for orbits and coorbits 375
§3 The ^ functional 382
3.1 Elementary properties of the K func
tional 382
3.2 The .K functional and nonlinear bounded
operators 386
3.3 The functors of orbits and the .K func¬
tional 389
3.4 The computation of the X functional in
special Banach couples 390
§4 The connection between the K functional and
quasi concave functions 396
4.1 The notion of a generating element of a
function 396
V
vi CONTENTS
4.2 The classification of weight sequences 399
§5 X monotone couples . 407
5.1 The classical X monotone couples 407
5.2 Interpolation from the couple L^iv) into
an arbitrary Banach couple 409
5.3 Interpolation from the couple
{L^iw0), L^wi)} into {LJoo),L,,(o ,)} 416
5.4 /£ monotone couples and the Fourier
transform 417
§6 Orbital equivalence 419
§7 The real methods of interpolation 421
7.1 The .K method 421
7.2 The / method 430
7.3 The connection between K and /
methods 432
7.4 Reiteration for the K and / methods 435
7.5 Duality between K and / methods 438
7.6 Special cases of K and / methods 441
7.7 A reiteration theorem connected with
functions of the type P+~ 447
§8 The interpolation methods of Ovchinnikov and
Gustavsson Peetre 449
8.1 Definition of functors 449
8.2 The Calderon construction of an inter¬
mediate space for a couple of Banach
lattices 452
8.3 Special properties of the functors Gu
G2, G3 464
8.4 Dual constructions 470
8.5 Computation of the spaces of the dual
constructions 474
CONTENTS vii
8.6 Reiteration theorems for functors G
and H 482
8.7 Functors commuting with infinite direct
products 485
8.8 Duality between the functors G and H 487
§9 Orbital description of the complex method 489
§10 Interpolation orbits of some special ideals 496
10.1 The orbits of coherently nuclear
operators 496
10.2 The interpolation orbits of the ideal AS^ 498
10.3 Orbits of ideals connected with the
couple {L,, Loo} 500
§11 Hilbert couples 505
11.1 Interpolation of operators in the
ideals Sp 505
11.2 Interpolation of nuclear operators con¬
nected with Hilbert couples 508
11.3 Some applications 510
11.4 The description of all Hilbert interpola¬
tion spaces for Hilbert couples 511
|
| any_adam_object | 1 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:27:15Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005903121 |
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| owner_facet | DE-29T DE-188 |
| physical | IX S., S. 349 - 515 |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Harwood |
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| series | Mathematical reports |
| series2 | Mathematical reports |
| spelling | Ovčinnikov, V. I. Verfasser aut The method of orbits in interpolation theory V. I. Ovchinnikov Chur [u.a.] Harwood 1984 IX S., S. 349 - 515 txt rdacontent n rdamedia nc rdacarrier Mathematical reports 1,2 Interpolationsoperator (DE-588)4162122-0 gnd rswk-swf Interpolationsoperator (DE-588)4162122-0 s DE-604 Mathematical reports 1,2 (DE-604)BV001892994 1,2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005903121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ovčinnikov, V. I. The method of orbits in interpolation theory Mathematical reports Interpolationsoperator (DE-588)4162122-0 gnd |
| subject_GND | (DE-588)4162122-0 |
| title | The method of orbits in interpolation theory |
| title_auth | The method of orbits in interpolation theory |
| title_exact_search | The method of orbits in interpolation theory |
| title_full | The method of orbits in interpolation theory V. I. Ovchinnikov |
| title_fullStr | The method of orbits in interpolation theory V. I. Ovchinnikov |
| title_full_unstemmed | The method of orbits in interpolation theory V. I. Ovchinnikov |
| title_short | The method of orbits in interpolation theory |
| title_sort | the method of orbits in interpolation theory |
| topic | Interpolationsoperator (DE-588)4162122-0 gnd |
| topic_facet | Interpolationsoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005903121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001892994 |
| work_keys_str_mv | AT ovcinnikovvi themethodoforbitsininterpolationtheory |