Sampling and Interpolating Sequences for Multiband-Limited Functions and Exponential Bases on Disconnected Sets.
Sampling and interpolation in the Paley-Wiener spaces Lπp, 0 < p ≤ 1.
Following Beurling's ideas concerning sampling and interpolation in the Paley-Wiener space Lτ∞, we find necessary and sufficient density conditions for sets of sampling and interpolation in the Paley-Wiener spaces Lτp for 0 < p ≤ 1.
Sampling Multipliers and the Poisson Summation Formula.
Sampling of Band-Limited Vectors.
Sampling on the Sierpinski gasket.
Sampling theory for functions with fractal spectrum.
Scale-dependent functions, stochastic quantization and renormalization.
Schauder decompositions and multiplier theorems
We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.
Schrödinger Equation and Oscillatory Hilbert Transforms of Second Degree.
Schrödinger equation on the Heisenberg group
Schwartz Kernels on Siegel II Domains.
Second order elliptic operators with complex bounded measurable coefficients in , Sobolev and Hardy spaces
Let be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with , such as the heat semigroup and Riesz transform, are not, in general, of Calderón-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in , Sobolev, and some new Hardy spaces naturally associated to . First, we show that the...
Self-affine measures that are -improving
A measure is called -improving if it acts by convolution as a bounded operator from to L² for some q < 2. Interesting examples include Riesz product measures, Cantor measures and certain measures on curves. We show that equicontractive, self-similar measures are -improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be -improving.
Self-Similar Lattice Tillings.
Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Semiclassical measures for the Schrödinger equation on the torus
In this article, the structure of semiclassical measures for solutions to the linear Schrödinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely continuous with respect to the Lebesgue measure. We obtain an expression of the Radon-Nikodym derivative in terms of the sequence of initial data and show that it satisfies an explicit propagation law. As a consequence, we also prove an observability inequality, saying...
Semi-groupes holomorphes et -convexité
Semi-groupes holomorphes et -convexité (suite)
Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains.
Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type Δu - N(x,u) = F(x), equipped with Dirichlet and Neumann boundary conditions.
Semiorthogonal linear prewavelets on irregular meshes
We extend results on constructing semiorthogonal linear spline prewavelet systems in one and two dimensions to the case of irregular dyadic refinement. In the one-dimensional case, we obtain sharp two-sided inequalities for the -condition, 1 < p < ∞, of such systems.