Three cases of normality of Hessenberg's matrix related with atomic complex distributions.
Three results in Dunkl analysis
We first establish a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the norm of Dunkl translations in dimension 1. Finally, we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.
Tight Frames of Multidimensional Wavelets.
Tiling and spectral properties of near-cubic domains
We prove that if a measurable domain tiles ℝ or ℝ² by translations, and if it is "close enough" to a line segment or a square respectively, then it admits a lattice tiling. We also prove a similar result for spectral sets in dimension 1, and give an example showing that there is no analogue of the tiling result in dimensions 3 and higher.
Time-frequency analysis of Sjöstrand's class.
We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.
Time-frequency representations : wavelet packets and optimal decomposition
Toeplitz Arrays, Linear Sequence Transformations and Orthogonal Polynomials.
Topics on analytic sets
Topological and algebraic genericity of divergence and universality
We give general theorems which assert that divergence and universality of certain limiting processes are generic properties. We also define the notion of algebraic genericity, and prove that these properties are algebraically generic as well. We show that universality can occur with Dirichlet series. Finally, we give a criterion for the set of common hypercyclic vectors of a family of operators to be algebraically generic.
Topological Dichotomy and Unconditional Convergence
In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.
Topological results on sequences and their applications in the theory of trigonometric series
Trace inequalities for fractional integrals in grand Lebesgue spaces
rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from to (trace inequality), where 1 < p < q < ∞, θ > 0 and μ satisfies the doubling condition in X. The results are new even for Euclidean spaces. For example, from our general results D. Adams-type necessary and sufficient conditions guaranteeing the trace inequality for fractional maximal functions and potentials defined on so-called s-sets in ℝⁿ follow. Trace inequalities...
Trace Inequalities, Maximal Inequalities, and Weighted Fourier Transform Estimates.
Trace theorems in harmonic function spaces on , multipliers theorems and related problems
Traces and the F. and M. Riesz theorem for vector fields
This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field . Applications to the F. and M. Riesz property for vector fields are discussed.
Traces of functions with a dominating mixed derivative in
We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in , with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to . The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.
Traces of Oscillating Functions.
Tractable embeddings of Besov spaces into Zygmund spaces
The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces. This can be expressed in terms of tractability envelopes.
Tractable embeddings of Besov spaces into Zygmund spaces, II
The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces.
Transference and restriction of maximal multiplier operators on Hardy spaces
The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces and , 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an function m is a maximal multiplier on if and only if it is a maximal multiplier on . As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered.