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Displaying similar documents to “Spectral synthesis and the Pompeiu problem”

On functions whose translates are independent

Ralph E. Edwards (1951)

Annales de l'institut Fourier

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Ce travail est l’étude de divers cas particuliers d’un problème nouveau, semble-t-il, concernant les translatées de fonctions ou de distributions sur un groupe. Soit E un espace vectoriel topologique de fonctions ou de distributions sur un groupe abélien G localement compact ; E est supposé invariant par les translations a → f a ( x ) = f ( x + a ) ( f ∈ E , a ∈ G ) . Si f ∈ E et si A est un sous-ensemble non vide de G , I ( f , A ) = I ( f , A , E ) désigne le sous-espace vectoriel fermé de E engendré par les translatées f a de f avec a ∈ A . On dira qu’une f ∈ E a ses...

On Ditkin sets

T. Muraleedharan, K. Parthasarathy (1996)

Colloquium Mathematicae

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In the study of spectral synthesis S-sets and C-sets (see Rudin [3]; Reiter [2] uses the terminology Wiener sets and Wiener-Ditkin sets respectively) have been discussed extensively. A new concept of Ditkin sets was introduced and studied by Stegeman in [4] so that, in Reiter’s terminology, Wiener-Ditkin sets are precisely sets which are both Wiener sets and Ditkin sets. The importance of such sets in spectral synthesis and their connection to the C-set-S-set problem (see Rudin [3])...

Construction of a certain superharmonic majorant

Paul Koosis (1994)

Annales de l'institut Fourier

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Given a function f ( t ) ≥ 0 on ℝ with ∫ - ∞ ∞ ( f ( t ) / ( 1 + t 2 ) ) d t < ∞ and | f ( t ) - f ( t ' ) | ≤ l | t - t ' | , a procedure is exhibited for obtaining on ℂ a (finite) superharmonic majorant of the function F ( z ) : 1 π ∫ - ∞ ∞ | 𝔍 z | | z - t | 2 f ( t ) d t - A l | 𝔍 z | , where A is a certain (large) absolute constant. This leads to fairly constructive proofs of the two main multiplier theorems of Beurling and Malliavin. The principal tool used is a version of the following lemma going back almost surely to Beurling: suppose that f ( t ) , positive and bounded away from 0 on ℝ , is such that ∫ - ∞ ∞ ( f ( t ) / ( 1 + t 2 ) d t < ∞ and denote,...

Formulae for joint spectral radii of sets of operators

Victor S. Shulman, Yuriĭ V. Turovskii (2002)

Studia Mathematica

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The formula ϱ ( M ) = m a x ϱ χ ( M ) , r ( M ) is proved for precompact sets M of weakly compact operators on a Banach space. Here ϱ(M) is the joint spectral radius (the Rota-Strang radius), ϱ χ ( M ) is the Hausdorff spectral radius (connected with the Hausdorff measure of noncompactness) and r(M) is the Berger-Wang radius.

L p - L q estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

Michael Cowling, Saverio Giulini, Stefano Meda (2001)

Annales de l’institut Fourier

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Let X be a symmetric space of the noncompact type, with Laplace–Beltrami operator - ℒ , and let [ b , ∞ ) be the L 2 ( X ) -spectrum of ℒ . For τ in ℂ such that Re τ ≥ 0 , let 𝒫 τ be the operator on L 2 ( X ) defined formally as exp ( - τ ( ℒ - b ) 1 / 2 ) . In this paper, we obtain L p - L q operator norm estimates for 𝒫 τ for all τ , and show that these are optimal when τ is small and when | arg τ | is bounded below π / 2 .

On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball

Nikolai Nikolov, Pascal J. Thomas (2008)

Annales Polonici Mathematici

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Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a “generalized” tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone C A to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.

An elementary proof of the Briançon-Skoda theorem

Jacob Sznajdman (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function φ belongs to an ideal I of the ring of germs of analytic functions at 0 ∈ ℂ n ; more precisely, the ideal membership is obtained if a function associated with φ and I is locally square integrable. If I can be generated by m elements,it follows in particular that I min ( m , n ) ¯ ⊂ I , where J ¯ denotes the integral closure of an ideal J .