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A semigroup analogue of the Fonf-Lin-Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis

Delio Mugnolo (2004)

Studia Mathematica

In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space X with a basis. (i) X is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on X is uniformly mean ergodic. (ii) X is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on X is mean ergodic.

A Simple Example of Localized Parametric Resonance for the Wave Equation

Colombini, Ferruccio, Rauch, Jeffrey (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.The problem studied here was suggested to us by V. Petkov. Since the beginning of our careers, we have benefitted from his insights in partial differential equations and mathematical physics. In his writings and many discussions, the conjuction of deep analysis and specially interesting problems has been a source inspiration for us.The research of J. Rauch is partially supported by the U.S. National Science Foundation under grant NSF-DMS-0104096...

A spectral mapping theorem for Banach modules

H. Seferoğlu (2003)

Studia Mathematica

Let G be a locally compact abelian group, M(G) the convolution measure algebra, and X a Banach M(G)-module under the module multiplication μ ∘ x, μ ∈ M(G), x ∈ X. We show that if X is an essential L¹(G)-module, then σ ( T μ ) = μ ̂ ( s p ( X ) ) ¯ for each measure μ in reg(M(G)), where T μ denotes the operator in B(X) defined by T μ x = μ ∘ x , σ(·) the usual spectrum in B(X), sp(X) the hull in L¹(G) of the ideal I X = f ∈ L ¹ ( G ) | T f = 0 , μ̂ the Fourier-Stieltjes transform of μ, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains all...

A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators A n , n ∈ ℕ , in a suitable Hilbert space. We show that the essential spectrum of A n is an interval of type [ γ , + ∞ [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An, n ∈ ℕ , in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type [ γ , + ∞ [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

A spectral theory for locally compact abelian groups of automorphisms of commutative Banach algebras

Sen Huang (1999)

Studia Mathematica

Let A be a commutative Banach algebra with Gelfand space ∆ (A). Denote by Aut (A) the group of all continuous automorphisms of A. Consider a σ(A,∆(A))-continuous group representation α:G → Aut(A) of a locally compact abelian group G by automorphisms of A. For each a ∈ A and φ ∈ ∆(A), the function φ a ( t ) : = φ ( α t a ) t ∈ G is in the space C(G) of all continuous and bounded functions on G. The weak-star spectrum σ w * ( φ a ) is defined as a closed subset of the dual group Ĝ of G. For φ ∈ ∆(A) we define Ʌ φ a to be the union of all...

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