Results 81 to 90 of about 184 (106)

Generalized Fourier expansion in kernels of convolution operators on Fourier hyperfunctions

Analysis (Germany), 2007
We prove that the kernels of surjective convolution operators on Fourier hyperfunctions (and on Fourier ultra-hyperfunctions) admit a basis of exponential solutions. The corresponding coefficient spaces are explicitly determined.
Michael Langenbruch
exaly   +3 more sources

Vector-valued Fourier hyperfunctions [PDF]

, 2014
This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a non-necessarily metrizable locally convex space E. Moreover, necessary and sufficient conditions are described such that a reasonable theory of E-valued Fourier hyperfunctions exists.
Kruse, Karsten
openaire   +2 more sources

Convolution and multiplication operators in Fourier hyperfunctions

Integral Transforms and Special Functions, 2006
We characterize the multiplication and convolution operators in the space ℱ′ of Fourier hyperfunctions. This generalizes the results of Schwartz on the multiplication and convolution operators on the space 𝒮′ of tempered distributions to the space ℱ′ of Fourier hyperfunctions.
Dohan Kim
exaly   +2 more sources

Fourier Transformation of Power-Type Hyperfunctions

Mathematics and Its Application Japanese Series, 1992
In the preceding chapter, we explained the basic facts about the Fourier transformation of hyperfunctions and showed methods of calculating Fourier transforms of some simple hyperfunctions. In this chapter, we shall be concerned with Fourier transforms of the power-type hyperfunctions ∣x∣α (log ∣x∣)n H(x), ∣x∣α(log ∣x∣)n, ∣x∣α(log ∣x∣)n sgn x (α ...
Isao Imai, Imai Isao
exaly   +2 more sources

THE SPACE OF FOURIER HYPERFUNCTIONS AS AN INDUCTIVE LIMIT OF HILBERT SPACES

Communications of the Korean Mathematical Society, 2004
Summary: We research properties of the space of measurable fun-ctions square integrable with weight \(\exp(2\nu|x|)\), and those of the space of Fourier hyperfunctions. Also we show that the several embedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hyperfunctions onto the ...
exaly   +3 more sources

Schwartz’ Kernel Theorem for Fourier Hyperfunctions [PDF]

, 2000
An appropriate general version of the kernel theorem of L. Schwartz is formulated for Fourier hyperfunctions and a direct functional analytic proof is presented. This talk is based on a joint paper [2] with S. Nagamachi.
E. Brüning
openaire   +2 more sources

Microlocalization within Some Classes of Fourier Hyperfunctions [PDF]

, 2006
New presheaves of hyperfunction spaces with the growth estimates with respect to |x| → ∞ and y → 0 in a cone Γ are introduced. Then it is shown that the Laplace transform is a bijective mapping of the space of tempered ultradistributions on R n of non-quasianalytic class onto the corresponding hyperfunction space of sections over D n, the ...
Richard D. Carmichael, Atsuhiko Eida, Stevan Pilipović   +2 more
openaire   +2 more sources

Hyperfunctions, formal groups and generalized Lipschitz summation formulas [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2012
a b s t r a c t A construction relating the theory of hyperfunctions with the theory of formal groups and generalizations of the classical Lipschitz summation formula is proposed.
Stefano Marmi, Piergiulio Tempesta
exaly   +4 more sources

Asymptotic Fourier and Laplace transformations for hyperfunctions

Studia Mathematica, 2011
Michael Langenbruch
exaly   +2 more sources

Fourier expansion of hyperfunctions on the circle [PDF]

, 1998
openaire   +2 more sources