Sigularity Spectrum of Multifractal Functions Involving Oscillating Singularities.
Single Wavelets in n-Dimensions.
Singular integrals with highly oscillating kernels on product spaces
We prove the boundedness of the oscillatory singular integrals for arbitrary real-valued functions and for rather general domains whose dependence upon x satisfies no regularity assumptions.
Size properties of wavelet packets generated using finite filters.
Skew-orthogonal polynomials of a discrete variable.
Smooth Local Sinusodial Bases on Two-Dimensional L-Shaped Regions.
Smoothing Minimally Supported Frequency Wavelets. Part I.
Smoothing Minimally Suppprted Frequency Wavelets: Part II.
Sobolev orthogonal polynomials: Interpolation and approximation.
Solutions to Deconvolution Equations Using Nonperiodic Sampling.
Solving dual integral equations on Lebesgue spaces
We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh’s type. We reformulate these equations giving a better description in terms of continuous operators on spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series which converges in the -norm and almost everywhere, where denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution....
Solving the axisymmetric inverse heat conduction problem by a wavelet dual least squares method.
Some applications and numerical methods for orthogonal polynomials
Some class of polynomial hypergroups
We provide explicit formulas for linearizing coefficients for some class of orthogonal polynomials.
Some classical function systems in separable Orlicz spaces
The boundedness of (sub)sequences of partial Fourier and Fourier-Walsh sums in subspaces of separable Orlicz spaces is studied. The boundedness of the shift operator and Paley function with respect to the Haar system is also investigated. These results are applied to get the analogues of the classical theorems on basicness of the trigonometric and Walsh systems in nonreflexive separable Orlicz spaces.
Some Coefficient Estimates for Polynomials on the Unit Interval
2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.In this paper we present some inequalities about the moduli of the coefficients of polynomials of the form f (x) : = еn = 0nan xn, where a0, ј, an О C. They can be seen as generalizations, refinements or analogues of the famous inequality of P. L. Chebyshev, according to which |an| Ј 2n-1 if | еn = 0n an xn | Ј 1 for -1 Ј x Ј 1.
Some counterexamples to subexponential growth of orthogonal polynomials
We give examples of polynomials p(n) orthonormal with respect to a measure μ on ⨍ such that the sequence {p(n,x)} has exponential lower bound for some points x of supp μ. Moreover, the set of such points is dense in the support of μ.
Some discrete representations of -classical linear forms.
Some eigenvalue estimates for wavelet related Toeplitz operators
By a straightforward computation we obtain eigenvalue estimates for Toeplitz operators related to the two standard reproducing formulas of the wavelet theory. Our result extends the estimates for Calderón-Toeplitz operators obtained by Rochberg in [R2]. In the first section we recall two standard reproducing formulas of the wavelet theory, we define Toeplitz operators and discuss some of their properties. The second section contains precise statements of our results and their proofs. At the end...
Some Essential Properties of Q...(...)-Spaces.