Asymptotic Expansions of Schwartz's Distributions
Asymptotic Fourier and Laplace transformations for hyperfunctions
We develop an elementary theory of Fourier and Laplace transformations for exponentially decreasing hyperfunctions. Since any hyperfunction can be extended to an exponentially decreasing hyperfunction, this provides simple notions of asymptotic Fourier and Laplace transformations for hyperfunctions, improving the existing models. This is used to prove criteria for the uniqueness and solvability of the abstract Cauchy problem in Fréchet spaces.
Asymptotic hyperfunctions, tempered hyperfunctions, and asymptotic expansions.
Asymptotics of regular convolution quotients.
Automatic Continuity of Generalized Local Linear Operators.
Automatische Stetigkeitseigenschaften einiger Klassen linearer Operatoren.
Automorphic forms, hyperfunction cohomology, and period functions.
Balanced Colombeau products of the distributions and
Results on singular products of the distributions and for natural are derived, when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.
Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions. Part II.
Bases in spaces of analytic germs
We prove precise decomposition results and logarithmically convex estimates in certain weighted spaces of holomorphic germs near ℝ. These imply that the spaces have a basis and are tamely isomorphic to the dual of a power series space of finite type which can be calculated in many situations. Our results apply to the Gelfand-Shilov spaces and for α > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.
Bases in Spaces of Ultradifferentiable Functions with Compact Support.
Beitrag zum Divisionsproblem für Ultradistributionen und ein Fortsetzungsansatz.
Between the Paley-Wiener theorem and the Bochner tube theorem
We present the classical Paley-Wiener-Schwartz theorem [1] on the Laplace transform of a compactly supported distribution in a new framework which arises naturally in the study of the Mellin transformation. In particular, sufficient conditions for a function to be the Mellin (Laplace) transform of a compactly supported distribution are given in the form resembling the Bochner tube theorem [2].
Beurling-Gevrey tempered ultradistributions as boundary values
Bieberbach functions and periodic distributions.
BMO-scale of distribution on
Let be the class of tempered distributions. For we denote by the Bessel potential of of order . We prove that if , then for any , , where , . Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order belongs to the space.
Boehmians of type S and their Fourier transforms
Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.
Boehmians on manifolds.
Borel's theorem for generalized functions
Boundary value problems for ordinary linear differential equations in the Colombeau algebra