Ueber die Entwickelung der doppelt periodischen Funktionen zweiter und dritter Art in trigonometrische Reihen. (Dritte Abhandlung)
Ueber die Integration der trigonometrischen Reihe
Ueber die Multiplication trigonometrischer Reihen
Ueber die trigonometrische Reihe und die Darstellung willkürlicher Functionen
Ueber eine gewisse Erweiterung des Cantor'schen Satzes
Ueber eine neue Eigenschaft der Laplace'schen Y(n) und ihre Anwendung zur analytischen Darstellung derjenigen Phänomene, welche Functionen der geographischen Länge und Breite sind. (Aus Schumacher's Astronomisc
Ueber einen die trigonometrischen Reihen betreffenden Lehrsatz.
Ueber trigonometrische Reihen
Un altro modo di costruire la serie di Fourier delle distribuzioni di una variabile quasi periodiche
Unbounded Lebesgue Constants on Compact Groups.
Uncertainty principles for integral operators
The aim of this paper is to prove new uncertainty principles for integral operators with bounded kernel for which there is a Plancherel Theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function is highly localized near a single point then (f) cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function and its integral...
Uncertainty principles for orthonormal bases
In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks...). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.Finally, we reformulate some uncertainty principles in terms of properties of the free heat and shrödinger equations.
Uncertainty principles revisited.
Unconditional biorthogonal wavelet bases in
We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces with 1 < p < ∞, provided the biorthogonal wavelet set functions satisfy weak decay conditions. The biorthogonal wavelet set is associated with an arbitrary dilation matrix in any dimension.
Unconditionality of general Franklin systems in , 1 < p < ∞
By a general Franklin system corresponding to a dense sequence = (tₙ, n ≥ 0) of points in [0,1] we mean a sequence of orthonormal piecewise linear functions with knots , that is, the nth function of the system has knots t₀, ..., tₙ. The main result of this paper is that each general Franklin system is an unconditional basis in , 1 < p < ∞.
Unconditionality of orthogonal spline systems in H¹
We give a simple geometric characterization of knot sequences for which the corresponding orthonormal spline system of arbitrary order k is an unconditional basis in the atomic Hardy space H¹[0,1].
Unconditionality of orthogonal spline systems in
We prove that given any natural number k and any dense point sequence (tₙ), the corresponding orthonormal spline system is an unconditional basis in reflexive .
Under which conditions is the Jacobi space subset of ?
Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property ⊂ is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.
Une classe d'ensembles d'unicité des séries trigonométriques
Une Formule Approximative de Dimension pour Certain Produits de Riesz.