Function spaces related to continuous negative definite functions: psi-Bessel potential spaces
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Warszawa
Inst. of Mathematics
2001
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| Series: | Dissertationes mathematicae
393 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 62 S. |
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Titel: Function spaces related to continuous negative definite functions
Autor: Farkas, Erich Walter
Jahr: 2001
CONTENTS
Introduction. 5
1. Auxiliary results .10
1.1. Negative definite functions and convolution semigroups .10
1.2. Bernstein functions and convolution semigroups supported in [0, oo) .15
1.3. One-parameter operator semigroups .18
1.4. Subordination in the sense of Bochner and a functional calculus for generators . 21
1.5. Sub-Markovian semigroups and abstract Bessel potential spaces.26
2. Bessel potential spaces associated with continuous negative definite functions .30
2.1. The space Hp2{Rn) as domain of A(p).31
2.2. The spaces.40
2.3. Embeddings for the spaces .46
2.4. Complex interpolation.52
2.5. Capacities and quasi-continuous modifications.55
References. 58
2000 Mathematics Subject Classification: Primary 46E35; Secondary 31C25, 35S99, 42B99,
47D07, 47G99, 60J45.
Key words and phrases: anisotropic Bessel potential spaces, subordination in the sense of Boch-
ner, Lp-potential theory, (r,p)-capacities, interpolation of operators.
Received 11.4.2000; final version 7.8.2000.
Acknowledgements. The first two named authors were supported through the DFG-project
Ja522/7-l Funktionenrdume in der Theorie der stochastischen Prozesse.
The third author gratefully acknowledges financial support through the Nuffield foundation,
grant NAL/00056/G.
Abstract
We introduce and systematically investigate Bessel potential spaces associated with a real-valued
continuous negative definite function. These spaces can be regarded as (higher order) invariants
of translation invariant Dirichlet spaces and in general they are not covered by known scales of
function spaces. We give equivalent norm characterizations, determine the dual spaces and prove
embedding theorems. Furthermore, complex interpolation spaces are calculated. Capacities are
introduced and the existence of quasi-continuous modifications is shown. |
| any_adam_object | 1 |
| author | Farkas, Walter Jacob, Niels 1955- Schilling, René L. 1969- |
| author_GND | (DE-588)141510129 (DE-588)122050045 |
| author_facet | Farkas, Walter Jacob, Niels 1955- Schilling, René L. 1969- |
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| bvnumber | BV013919619 |
| classification_rvk | SI 390 |
| classification_tum | MAT 336d |
| ctrlnum | (OCoLC)163832815 (DE-599)BVBBV013919619 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2025-02-25T11:05:07Z |
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| physical | 62 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Inst. of Mathematics |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Farkas, Walter Verfasser aut Function spaces related to continuous negative definite functions psi-Bessel potential spaces Walter Farkas, Niels Jacob and René L. Schilling Warszawa Inst. of Mathematics 2001 62 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 393 Jacob, Niels 1955- Verfasser (DE-588)141510129 aut Schilling, René L. 1969- Verfasser (DE-588)122050045 aut Dissertationes mathematicae 393 (DE-604)BV000003039 393 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009524078&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farkas, Walter Jacob, Niels 1955- Schilling, René L. 1969- Function spaces related to continuous negative definite functions psi-Bessel potential spaces Dissertationes mathematicae |
| title | Function spaces related to continuous negative definite functions psi-Bessel potential spaces |
| title_auth | Function spaces related to continuous negative definite functions psi-Bessel potential spaces |
| title_exact_search | Function spaces related to continuous negative definite functions psi-Bessel potential spaces |
| title_full | Function spaces related to continuous negative definite functions psi-Bessel potential spaces Walter Farkas, Niels Jacob and René L. Schilling |
| title_fullStr | Function spaces related to continuous negative definite functions psi-Bessel potential spaces Walter Farkas, Niels Jacob and René L. Schilling |
| title_full_unstemmed | Function spaces related to continuous negative definite functions psi-Bessel potential spaces Walter Farkas, Niels Jacob and René L. Schilling |
| title_short | Function spaces related to continuous negative definite functions |
| title_sort | function spaces related to continuous negative definite functions psi bessel potential spaces |
| title_sub | psi-Bessel potential spaces |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009524078&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
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