# In search of the invisible spectrum

Annales de l'institut Fourier (1999)

- Volume: 49, Issue: 6, page 1925-1998
- ISSN: 0373-0956

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topNikolski, Nikolai. "In search of the invisible spectrum." Annales de l'institut Fourier 49.6 (1999): 1925-1998. <http://eudml.org/doc/75407>.

@article{Nikolski1999,

abstract = {In this paper, we begin the study of the phenomenon of the “invisible spectrum” for commutative Banach algebras. Function algebras, formal power series and operator algebras will be considered. A quantitative treatment of the famous Wiener-Pitt-Sreider phenomenon for measure algebras on locally compact abelian (LCA) groups is given. Also, our approach includes efficient sharp estimates for resolvents and solutions of higher Bezout equations in terms of their spectral bounds. The smallest “spectral hull” of a given closed set is introduced and studied; it permits the definition of a uniformly bounded functional calculus. In this paper, the program traced above is realized for the following algebras: the measure algebras of LCA groups; the measure algebras of a large class of topological abelian semigroups; their subalgebras - the (semi)group algebra of LCA (semi)groups, the algebra of almost periodic functions, the algebra of absolutely convergent Dirichlet series. Upper and lower estimates for the best majorants and critical constants are obtained.},

author = {Nikolski, Nikolai},

journal = {Annales de l'institut Fourier},

keywords = {invisible spectrum; LCA groups; measure algebra; Wiener-Pitt-Sreider phenomenon; norm controlled inversion; cyclic groups; spectral hulls; function algebras; norm-controlled functional calculi; commutative Banach algebras; formal power series; operator algebras; Bézout equations; algebra of almost periodic functions; algebra of absolutely convergent Dirichlet series; best majorants; critical constants},

language = {eng},

number = {6},

pages = {1925-1998},

publisher = {Association des Annales de l'Institut Fourier},

title = {In search of the invisible spectrum},

url = {http://eudml.org/doc/75407},

volume = {49},

year = {1999},

}

TY - JOUR

AU - Nikolski, Nikolai

TI - In search of the invisible spectrum

JO - Annales de l'institut Fourier

PY - 1999

PB - Association des Annales de l'Institut Fourier

VL - 49

IS - 6

SP - 1925

EP - 1998

AB - In this paper, we begin the study of the phenomenon of the “invisible spectrum” for commutative Banach algebras. Function algebras, formal power series and operator algebras will be considered. A quantitative treatment of the famous Wiener-Pitt-Sreider phenomenon for measure algebras on locally compact abelian (LCA) groups is given. Also, our approach includes efficient sharp estimates for resolvents and solutions of higher Bezout equations in terms of their spectral bounds. The smallest “spectral hull” of a given closed set is introduced and studied; it permits the definition of a uniformly bounded functional calculus. In this paper, the program traced above is realized for the following algebras: the measure algebras of LCA groups; the measure algebras of a large class of topological abelian semigroups; their subalgebras - the (semi)group algebra of LCA (semi)groups, the algebra of almost periodic functions, the algebra of absolutely convergent Dirichlet series. Upper and lower estimates for the best majorants and critical constants are obtained.

LA - eng

KW - invisible spectrum; LCA groups; measure algebra; Wiener-Pitt-Sreider phenomenon; norm controlled inversion; cyclic groups; spectral hulls; function algebras; norm-controlled functional calculi; commutative Banach algebras; formal power series; operator algebras; Bézout equations; algebra of almost periodic functions; algebra of absolutely convergent Dirichlet series; best majorants; critical constants

UR - http://eudml.org/doc/75407

ER -

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