Tauberian theorem for the distributional Stieltjes transformation.
Taylor formula for distributions [Book]
The Bessel-Struve intertwining operator on and mean-periodic functions.
The bilinear Hilbert trasform is pointwise finite.
Let f ∈ L∞ and g ∈ L2 be supported on [0,1]. Then the principal value integral below exists in L1.p.v. ∫ f(x + y) g(x - y) dy / y.
The class of convolution operators on the Marcinkiewicz spaces
Let denote the operator-norm closure of the class of convolution operators where is a suitable function space on . Let be the closed subspace of regular functions in the Marinkiewicz space , . We show that the space is isometrically isomorphic to and that strong operator sequential convergence and norm convergence in coincide. We also obtain some results concerning convolution operators under the Wiener transformation. These are to improve a Tauberian theorem of Wiener on .
The continuous Jacobi transform.
The continuous Legendre transform, its inverse transform, and applications.
The distributional 1F1-Transform.
The Dunkl transform.
The equivalence of two conditions for weight functions
The Fourier transforms of Lipschitz functions on the Heisenberg group.
The general chain transform and self-reciprocal functions.
The generalizations of integral analog of the Leibniz rule on the G-convolutions.
An integral analog of the Leibniz rule for the operators of fractional calculus was considered in paper [1]. These operators are known to belong to the class of convolution transforms [2]. It seems very natural to try to obtain some new integral analog of the Leibniz rule for other convolution operators. We have found a general method for constructing such integral analogs on the base of notion of G-convolution [4]. Several results obtained by this method are represented in this article.
The generalized Airy diffusion equation.
The generalized sampling theorem for transforms of not necessarily square integrable functions.
The heat transform and its use in thermal identification problems for electronic circuits.
The Hilbert transform and maximal function along nonconvex curves in the plane.
In this paper we study the Hilbert transform and maximal function related to a curve in R2.
The Hilbert transform in weighted spaces of integrable vector-valued functions
The Identification Problem for the Constantly Attenuated Radon Transform.
The inversion formulae for some Bessel and hypergeometric