On the structure of Mellin distributions
On the two weights problem for the Hilbert transform.
In this paper, we prove sufficient conditions on pairs of weights (u,v) (scalar, matrix or operator valued) so that the Hilbert transform H f(x) = p.v. ∫ [f(y) / x - y] dy,is bounded from L2(u) to L2(v).
On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces
2000 Mathematics Subject Classification: 44A15, 44A35, 46E30In this paper we prove that the partial Dunkl integral ST(f) of f converges to f, as T → +∞ in L^∞(νµ) and we show that the Dunkl transform Fµ(f) of f is in L^1(νµ) when f belongs to a suitable Besov-Dunkl space. We also give sufficient conditions on a function f in order that the Dunkl transform Fµ(f) of f is in a L^p -space.* Supported by 04/UR/15-02.
On two new characterizations of Stieltjes transforms for distributions.
Operational calculi for Kontorovich-Lebedev and Mehler-Fock transforms on distributions with compact support.
Operational calculus for the continuous Legendre transform with applications.
Operational properties of a generalized Hermite transformation.
Operators associated with representations of amenable groups singular integrals induced by ergodic flows, the rotation method and multipliers
Paley-Wiener theorems for the Mellin transformation
Paley-Wiener-type theorem for a class of integral transforms arising from a singular Dirac system.
Planar harmonic univalent and related mappings.
Polynomial approach to conversion between Laplace and transforms
Properties of the L function
Pseudodifferential operators and Hardy kernels on
Quadrature Formulas for Oscillatory Integral Transforms.
Quasiasymptotic expansion of distributions from and the asymptotic expansion of the distributional Stieltjes transform.
Recent developments on the Stieltjes transform of generalized functions.
Representation of functions as the Post-Widder inversion operator of generalized functions.
Ridgelet transform on tempered distributions
We prove that ridgelet transform and adjoint ridgelet transform are continuous, where . We also define the ridgelet transform on the space of tempered distributions on , adjoint ridgelet transform on and establish that they are linear, continuous with respect to the weak-topology, consistent with , respectively, and they satisfy the identity , .
Semigroup theory applied to options.