Laplace transform of distribution-valued functions and its applications
Laplace transform of Laplace hyperfunctions and its applications.
Laplace ultradistributions on a half line and a strong quasi-analyticity principle
Several representations of the space of Laplace ultradistributions supported by a half line are given. A strong version of the quasi-analyticity principle of Phragmén-Lindelöf type is derived.
Laplace ultradistributions supported by a cone
The space of Laplace ultradistributions supported by a convex proper cone is introduced. The Seeley type extension theorem for ultradifferentiable functions is proved. The Paley-Wiener-Schwartz type theorem for Laplace ultradistributions is shown. As an application, the structure theorem and the kernel theorem for this space of ultradistributions are given.
Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces
We collect and extend results on the limit of as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ 0,1, l ∈ ℕ, p ∈ [1,∞), and is the intrinsic seminorm of order l+σ in the Sobolev space . In general, the above limit is equal to , where c and [·] are, respectively, a constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.
Linear and bilinear Hilbert transform.
Multipliers of Hankel transformable generalized functions
Let be the Zemanian space of Hankel transformable functions, and let be its dual space. In this paper is shown to be nuclear, hence Schwartz, Montel and reflexive. The space , also introduced by Zemanian, is completely characterized as the set of multipliers of and of . Certain topologies are considered on , and continuity properties of the multiplication operation with respect to those topologies are discussed.
New characterizations for Hankel transformable spaces of Zemanian.
New inversion formulas for the Krätzel transformation.
On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.
We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operatorAx = x2 - x d/dx [x d/dx],and its k-th iterates Akx, where k = 0, 1, ... , and A0xφ = φ. Comparing with other testing-function spaces, we introduce in its dual the Kontorovich-Lebedev transformation for distributions with respect to a complex index. The existence, uniqueness, imbedding and inversion properties are investigated. As an application we find a solution...
On Calderón's conjecture.
On extension of Gabor transform to Boehmians
On functional equations of complex powers.
On generation and propagation of tsunamis in a shallow running ocean.
On Hankel transform and Hankel convolution of Beurling type distributions having upper bounded support
In this paper we study Beurling type distributions in the Hankel setting. We consider the space of Beurling type distributions on having upper bounded support. The Hankel transform and the Hankel convolution are studied on the space . We also establish Paley Wiener type theorems for Hankel transformations of distributions in .
On Hankel transformable distribution spaces.
On Malgrange Theorem for Nuclear Holomorphic Functions in Open Balls of a Banach Space.
On Multidimensional Generalizations Of Regularly Varying Functions And Tauberian And Abelian Theorems
On multiplication of some generalized functions
On some classes of infinitely decomposable Sobolev-Schwartz test functions