Displaying similar documents to “On the spectral bound of the generator of a C 0 -semigroup”

Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator

Robert Haller-Dintelmann, Julian Wiedl (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on d , we define the notion of Kolmogorov kernel estimates. This allows us to show that under Dirichlet boundary conditions Ornstein-Uhlenbeck operators are generators of consistent, positive, (quasi-) contractive C 0 -semigroups on L p ( Ω ) for all 1 p < and for every domain Ω d . For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given. ...

On a function that realizes the maximal spectral type

Krzysztof Frączek (1997)

Studia Mathematica

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We show that for a unitary operator U on L 2 ( X , μ ) , where X is a compact manifold of class C r , r , ω , and μ is a finite Borel measure on X, there exists a C r function that realizes the maximal spectral type of U.

Spectral decompositions and harmonic analysis on UMD spaces

Earl Berkson, T. Gillespie (1994)

Studia Mathematica

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We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for L X p to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X. ...

Functional calculi, regularized semigroups and integrated semigroups

Ralph deLaubenfels, Mustapha Jazar (1999)

Studia Mathematica

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We characterize closed linear operators A, on a Banach space, for which the corresponding abstract Cauchy problem has a unique polynomially bounded solution for all initial data in the domain of A n , for some nonnegative integer n, in terms of functional calculi, regularized semigroups, integrated semigroups and the growth of the resolvent in the right half-plane. We construct a semigroup analogue of a spectral distribution for such operators, and an extended functional calculus: When...

Semigroups with nonquasianalytic growth

Phóng Vũ (1993)

Studia Mathematica

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We study asymptotic behavior of C 0 -semigroups T(t), t ≥ 0, such that ∥T(t)∥ ≤ α(t), where α(t) is a nonquasianalytic weight function. In particular, we show that if σ(A) ∩ iℝ is countable and Pσ(A*) ∩ iℝ is empty, then l i m t 1 / α ( t ) T ( t ) x = 0 , ∀x ∈ X. If, moreover, f is a function in L α 1 ( + ) which is of spectral synthesis in a corresponding algebra L α 1 1 ( ) with respect to (iσ(A)) ∩ ℝ, then l i m t 1 / α ( t ) T ( t ) f ̂ ( T ) = 0 , where f ̂ ( T ) = ʃ 0 f ( t ) T ( t ) d t . Analogous results are obtained also for iterates of a single operator. The results are extensions of earlier results of...

Injective semigroup-algebras

J. Green (1998)

Studia Mathematica

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Semigroups S for which the Banach algebra 1 ( S ) is injective are investigated and an application to the work of O. Yu. Aristov is described.

Closed semistable operators and singular differential equations

Jaromír J. Koliha, Trung Dinh Tran (2003)

Czechoslovak Mathematical Journal

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We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which 0 is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of C 0 -semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions...

Spectral radius formula for commuting Hilbert space operators

Vladimír Muller, Andrzej Sołtysiak (1992)

Studia Mathematica

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A formula is given for the (joint) spectral radius of an n-tuple of mutually commuting Hilbert space operators analogous to that for one operator. This gives a positive answer to a conjecture raised by J. W. Bunce in [1].

On spectral representation for selfadjoint operators. Expansion in generalized eigenelements

Eberhard Gerlach (1965)

Annales de l'institut Fourier

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L’auteur reprend l’étude classique de la représentation spectrale d’un opérateur auto-adjoint A dans un espace de Hilbert . Il y ajoute des précisions nouvelles qui conduisent à la définition du projecteur infinitésimal P ) λ ) sur l’espace des vecteurs propres généralisés ( λ ) . Il obtient, par conséquent, des énoncés plus précis de bien des théorèmes classiques. Il introduit ensuite la notion de “ A -expansibilité” d’un sous-ensemble S . Cette notion est appliquée à l’étude des espaces fonctionnels...