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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction........................................................................................5
1. Main definitions and basic examples..............................................7
2. Closed ideals in Sobolev algebras...............................................10
2.0. Notation...................................................................................10
2.1. Preliminary observations and results.......................................11
2.2. Closed primary ideals..............................................................13
2.3. Spectral synthesis of ideals.....................................................15
3. Spectral synthesis of ideals in the algebras $C^m Lip φ$............18
4. D-algebras...................................................................................21
5. Zygmund algebras.......................................................................26
5.1. Basic properties.......................................................................26
5.2. Extensions, approximations, and traces...................................32
5.3. Closed primary ideals...............................................................40
5.4. Point derivations......................................................................43
5.5. An extension property and spectral synthesis..........................46
5.6. Proof of Theorem 5.1...............................................................48
Appendix..........................................................................................52
1. Traces of generalized Lipschitz spaces.......................................53
2. Traces of Zygmund spaces.........................................................58
3. Proof of Proposition 5.2.11..........................................................62
References.......................................................................................65
Introduction........................................................................................5
1. Main definitions and basic examples..............................................7
2. Closed ideals in Sobolev algebras...............................................10
2.0. Notation...................................................................................10
2.1. Preliminary observations and results.......................................11
2.2. Closed primary ideals..............................................................13
2.3. Spectral synthesis of ideals.....................................................15
3. Spectral synthesis of ideals in the algebras $C^m Lip φ$............18
4. D-algebras...................................................................................21
5. Zygmund algebras.......................................................................26
5.1. Basic properties.......................................................................26
5.2. Extensions, approximations, and traces...................................32
5.3. Closed primary ideals...............................................................40
5.4. Point derivations......................................................................43
5.5. An extension property and spectral synthesis..........................46
5.6. Proof of Theorem 5.1...............................................................48
Appendix..........................................................................................52
1. Traces of generalized Lipschitz spaces.......................................53
2. Traces of Zygmund spaces.........................................................58
3. Proof of Proposition 5.2.11..........................................................62
References.......................................................................................65
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 46J20: Ideals, maximal ideals, boundaries
- 46H10: Ideals and subalgebras
- 46J10: Banach algebras of continuous functions, function algebras
- 41A10: Approximation by polynomials
- 26A16: Lipschitz (H\"older) classes
- 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
- 46E25: Rings and algebras of continuous, differentiable or analytic functions
- 46J15: Banach algebras of differentiable or analytic functions, H p -spaces
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
371
Liczba stron
67
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXXI
Daty
wydano
1997
otrzymano
1996-10-09
poprawiono
1997-02-20
Twórcy
autor
- Department of Mathematics, Idaho State University, Pocatello, Idaho 83209, U.S.A.
Bibliografia
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Języki publikacji
| EN |
Uwagi
1991 Mathematics Subject Classification: Primary 46E25, 46E35, 46H10, 46J10, 46J15, 46J20; Secondary 26A16, 41A10.
Identyfikator YADDA
bwmeta1.element.zamlynska-369d309c-6f8e-43cb-96b4-7ffbcf995e48
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki
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