A general Hilbert space approach to framelets.
A generalization of Bateman's expansion and finite integrals of Sonine's and Feldheim's type
Let be a sequence of arbitrary complex numbers, let α,β > -1, let Pₙα,βn=0+∞
A generalization of Riesz-Fischer theorem
A generalized strange term in Signorini’s type problems
The limit behavior of the solutions of Signorini’s type-like problems in periodically perforated domains with period is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as . In the critical case, it is shown that Signorini’s problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming from the...
A Generalized Strange Term in Signorini's Type Problems
The limit behavior of the solutions of Signorini's type-like problems in periodically perforated domains with period ε is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as ε → 0. In the critical case, it is shown that Signorini's problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming from...
A geometrical solution of a problem on wavelets
We prove the existence of nonseparable, orthonormal, compactly supported wavelet bases for of arbitrarily high regularity by using some basic techniques of algebraic and differential geometry. We even obtain a much stronger result: “most” of the orthonormal compactly supported wavelet bases for , of any regularity, are nonseparable
A gradient-projective basis of compactly supported wavelets in dimension n > 1
A given set W = W X of n-variable class C 1 functions is a gradient-projective basis if for every tempered distribution f whose gradient is square-integrable, the sum converges to f with respect to the norm . The set is not necessarily an orthonormal set; the orthonormal expansion formula is just an element of the convex set of valid expansions of the given function f over W. We construct a gradient-projective basis W = W x of compactly supported class C 2−ɛ functions on ℝn such that [...]...
A martingale approach to general Franklin systems
We prove unconditionality of general Franklin systems in , where X is a UMD space and where the general Franklin system corresponds to a quasi-dyadic, weakly regular sequence of knots.
A multiplier theorem for Jacobi expansions
A multiplier theorem for the Hankel transform.
Riesz function technique is used to prove a multiplier theorem for the Hankel transform, analogous to the classical Hörmander-Mihlin multiplier theorem (Hörmander (1960)).
A Necessary and Sufficient Condition for Dual Weyl-Heisenberg Frames to be Comactly Supported.
A necessary and sufficient condition for the existence of a father wavelet
A new approach to the problem of constructing recurrence relations for the Jacobi coefficients
A New Class of Unbalanced Haar Wavelets That Form an Unconditional Basis for L... on General Measure Spaces.
A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces [Book]
A new proof of a theorem about generalized orthogonal polynomials.
A new technique to estimate the regularity of refinable functions.
We study the regularity of refinable functions by analyzing the spectral properties of special operators associated to the refinement equation; in particular, we use the Fredholm determinant theory to derive numerical estimates for the spectral radius of these operators in certain spaces. This new technique is particularly useful for estimating the regularity in the cases where the refinement equation has an infinite number of nonzero coefficients and in the multidimensional cases.
A note on a one-parameter family of Catalan-like numbers.
A note on weights: Pasting weights and changing variables.
A note on certain partial sum operators
We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.