Riordan arrays, orthogonal polynomials as moments, and Hankel transforms.
Rodrigues-type formulae for Hermite and Laguerre polynomials.
Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions.
Let H be a closed subgroup of the group of rotation of Rn. The subspaces of distributions of Besov-Lizorkin-Triebel type invariant with respect to natural action of H are investigated. We give sufficient and necessary conditions for the compactness of the Sobolev-type embeddings. It is also proved that H-invariance of function implies its decay properties at infinity as well as the better local smoothness. This extends the classical Strauss lemma. The main tool in our investigations is an adapted...
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.
Self-Similar Lattice Tillings.
Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
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.
Séries de Fourier et séries d'ondelettes
Shannon wavelets theory.
Shannon's sampling theorem, incongruent residue classes and Plancherel's theorem
Sampling theory for multi-band signals is shown to have a logical structure similar to that of Fourier analysis.
Shape functions and wavelets - tools of numerical approximation
Solution of a boundary value problem is often realized as the application of the Galerkin method to the weak formulation of given problem. It is possible to generate a trial space by means of splines or by means of functions that are not polynomial and have compact support. We restrict our attention only to RKP shape functions and compactly supported wavelets. Common features and comparison of approximation properties of these functions will be studied in the contribution.
Sharp estimates of the Jacobi heat kernel
The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the other two classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters α, β ≥ -1/2. Using quite different methods, Coulhon, Kerkyacharian and Petrushev recently also obtained such estimates. As an application of the bounds, we show that...
Sidon sets and Riesz sets for some measure algebras on the disk
Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.
Signals generated in memristive circuits
Signals generated in circuits that include nano-structured elements typically have strongly distinct characteristics, particularly the hysteretic distortion. This is due to memristance, which is one of the key electronic properties of nanostructured materials. In this article, we consider signals generated from a memrsitive circuit model. We demonstrate numerically that such signals can be efficiently represented in certain custom-designed nonorthogonal bases. The proposed method ensures that the...