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Sommation effective d’une somme de Borel par séries de factorielles

Eric Delabaere, Jean-Marc Rasoamanana (2007)

Annales de l’institut Fourier

Nous abordons dans cet article la question de la sommation effective d’une somme de Borel d’une série par la série de factorielles associée. Notre approche fournit un contrôle de l’erreur entre la somme de Borel recherchée et les sommes partielles de la série de factorielles. Nous généralisons ensuite cette méthode au cadre des séries de puissances fractionnaires, après avoir démontré un analogue d’un théorème de Nevanlinna de sommation de Borel fine pour ce cadre.

Sous-ensembles de courbes Ahlfors-régulières et nombres de Jones.

Hervé Pajot (1996)

Publicacions Matemàtiques

We prove that an Ahlfors-regular set (with dimension one) E ⊂ Rn which verifies a βq-version of P. W. Jones' geometric lemma is included in an Ahlfors-regular curve Γ.This theorem is due to G. David and S. Semmes, we give a more direct proof.

Sous-espaces fermés de séries universelles sur un espace de Fréchet

Quentin Menet (2011)

Studia Mathematica

We improve a result of Charpentier [Studia Math. 198 (2010)]. We prove that even on Fréchet spaces with a continuous norm, the existence of only one restrictively universal series implies the existence of a closed infinite-dimensional subspace of restrictively universal series.

Spaces of sequences, sampling theorem, and functions of exponential type

Rodolfo Torres (1991)

Studia Mathematica

We introduce certain spaces of sequences which can be used to characterize spaces of functions of exponential type. We present a generalized version of the sampling theorem and a "nonorthogonal wavelet decomposition" for the elements of these spaces of sequences. In particular, we obtain a discrete version of the so-called φ-transform studied in [6] [8]. We also show how these new spaces and the corresponding decompositions can be used to study multiplier operators on Besov spaces.

Spectral approximation for Segal-Bargmann space Toeplitz operators

Albrecht Böttcher, Hartmut Wolf (1997)

Banach Center Publications

Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk N or on the Segal-Bargmann space over ℂ N . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression A n of A to the linear span of the monomials z 1 k 1 . . . z N k N : 0 ≤ k j ≤ n . Unfortunately, in general the spectrum of A n does not mimic the spectrum of A as...

Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem.

Marek Rakowski, Ilya Spitkovsky (1996)

Revista Matemática Iberoamericana

We define spectral factorization in Lp (or a generalized Wiener-Hopf factorization) of a measurable singular matrix function on a simple closed rectifiable contour Γ. Such factorization has the same uniqueness properties as in the nonsingular case. We discuss basic properties of the vector valued Riemann problem whose coefficient takes singular values almost everywhere on Γ. In particular, we introduce defect numbers for this problem which agree with the usual defect numbers in the case of a nonsingular...

Spectral theory of translation surfaces : A short introduction

Luc Hillairet (2009/2010)

Séminaire de théorie spectrale et géométrie

We define translation surfaces and, on these, the Laplace operator that is associated with the Euclidean (singular) metric. This Laplace operator is not essentially self-adjoint and we recall how self-adjoint extensions are chosen. There are essentially two geometrical self-adjoint extensions and we show that they actually share the same spectrum

Spirallike mappings and univalent subordination chains in ℂ n

Ian Graham, Hidetaka Hamada, Gabriela Kohr, Mirela Kohr (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we consider non-normalized univalent subordination chains and the connection with the Loewner differential equation on the unit ball in ℂ n . To this end, we study the most general form of the initial value problem for the transition mapping, and prove the existence and uniqueness of solutions. Also we introduce the notion of generalized spirallikeness with respect to a measurable matrix-valued mapping, and investigate this notion from the point of view of non-normalized univalent subordination...

Currently displaying 281 – 300 of 561