Tauberian and Abelian theorems for rapidly decaying distributions and their applications to stable laws.
Tauberian theorem for the distributional Stieltjes transformation.
Tauberian Theorems and Limit Distributions for Upper Order Statistics
Tauberian theorems for generalized functions in the scale of regularly varying functions and functionals.
Tauberian theorems for Laplace transforms.
Tauberian theorems for Laplace transforms in dimension D > 1.
Tauberian theorems for vector-valued Fourier and Laplace transforms
Let X be a Banach space and be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.
Taylor formula for distributions [Book]
The algebra of polynomials on the space of ultradifferentiable functions
We consider the space of ultradifferentiable functions with compact supports and the space of polynomials on . A description of the space of polynomial ultradistributions as a locally convex direct sum is given.
The analysis of a class of exponential operation functions.
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 Calderón Reproducing Formula, Windowed X-Ray Transforms, and Radon Transforms in L...-Spaces.
The class Bpfor weighted generalized Fourier transform inequalities
In the present paper, we prove weighted inequalities for the Dunkl transform (which generalizes the Fourier transform) when the weights belong to the well-known class Bp. As application, we obtain the Pitt’s inequality for power weights.
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 Closure In The Space Of Mikusinski's Operators
The closure in the space of Mikusinski's operators.
The continuous Jacobi transform.
The continuous Legendre transform, its inverse transform, and applications.
The convolution on time scales.