A non-linear theory of infrahyperfunctions [PDF]
, 2019 We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. H\"{o}rmander). In the hyperfunction case our work can be summarized as follows.
Debrouwere, Andreas +2 more
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Stability of Trigonometric Functional Equations in Generalized Functions
Journal of Inequalities and Applications, 2010 We consider the Hyers-Ulam stability of a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.
Jeongwook Chang, Jaeyoung Chung
doaj +2 more sources
Stability of Quartic Functional Equations in the Spaces of Generalized Functions
Advances in Difference Equations, 2009 We consider the general solution of quartic functional equations and prove the Hyers-Ulam-Rassias stability. Moreover, using the pullbacks and the heat kernels we reformulate and prove the stability results of quartic functional equations in the spaces ...
Chung Soon-Yeong, Lee Young-Su
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Rotation invariant ultradistributions [PDF]
, 2017 We prove that an ultradistribution is rotation invariant if and only if it coincides with its spherical mean. For it, we study the problem of spherical representations of ultradistributions on $\mathbb{R}^{n}$. Our results apply to both the quasianalytic
Vindas Diaz, Jasson, Vuckovic, Dorde
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Fibrational induction rules for initial algebras [PDF]
, 2010 This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors.
B. Jacobs +7 more
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Ulam Problem for the Cosine Addition Formula in Sato Hyperfunctions
Journal of Function Spaces, 2015 We prove the Ulam problem for the cosine addition formula in the spaces of Schwartz distributions and Sato hyperfunctions with respect to bounded distributions and bounded hyperfunctions.
Jaeyoung Chung, Soon-Yeong Chung
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Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions
Journal of Inequalities and Applications, 2008 Making use of the pullbacks, we reformulate the following quadratic functional equation: in the spaces of generalized functions. Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam ...
Lee Young-Su
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Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces [PDF]
, 2015 We study boundary values of holomorphic functions in translation-invariant distribution spaces of type $\mathcal{D}'_{E'_{\ast}}$. New edge of the wedge theorems are obtained.
Dimovski, Pavel +2 more
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The short-time Fourier transform of distributions of exponential type and Tauberian theorems for shift-asymptotics [PDF]
, 2016 We study the short-time Fourier transform on the space $\mathcal{K}_{1}'(\mathbb{R}^n)$ of distributions of exponential type. We give characterizations of $\mathcal{K}_{1}'(\mathbb{R}^n)$ and some of its subspaces in terms of modulation spaces.
Kostadinova, Sanja +3 more
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Towards a Generalized Distribution Formalism for Gauge Quantum Fields
, 1994 We prove that the distributions defined on the Gelfand-Shilov spaces, and hence more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables one to develop a
A. I. Oksak +22 more
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