Global pseudodifferential operators in spaces of ultradifferentiable functions [PDF]
, 2021 [ES] En esta tesis estudiamos operadores pseudodiferenciales, que son operadores integrales de la forma f 7→ ∫ Rd (∫ Rd ei(x−y)·ξa(x,y,ξ)f(y)dy)dξ, en las clases globales de funciones ultradiferenciables de tipo Beurling Sω(Rd) introducidas por Björck ...
Asensio López, Vicente
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Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019 [EN] We develop a theory of pseudodifferential operators of infinite order for the global classes S. of ultradifferentiable functions in the sense of Bjorck, following the previous ideas given by Prangoski for ultradifferentiable classes in the sense of ...
AA Albanese +16 more
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Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces [PDF]
, 2016 We introduce and study a number of new spaces of ultradifferentiable functions and ultradistributions and we apply our results to the study of the convolution of ultradistributions.
Dimovski, Pavel +3 more
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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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On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution [PDF]
, 2017 We develop a convolution theory for quasianalytic ultradistributions of Gelfand-Shilov type. We also construct a special class of ultrapolynomials, and use it as a base for the parametrix method in the study of new topological and structural properties ...
Pilipovic, Stevan +2 more
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Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp‐Growth
International Journal of Mathematics and Mathematical Sciences, Volume 2014, Issue 1, 2014., 2014 Let C be a regular cone in ℝ and let TC = ℝ + iC ⊂ ℂ be a tubular radial domain. Let U be the convolutor in Beurling ultradistributions of Lp‐growth corresponding to TC. We define the Cauchy and Poisson integral of U and show that the Cauchy integral of U is analytic in TC and satisfies a growth property.
Byung Keun Sohn, Shyam L. Kalla
wiley +1 more source
On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We study a family of singularly perturbed q‐difference‐differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter ϵ. Moreover, we achieve the existence of a common formal power series in ϵ which represents each actual solution and establish q‐Gevrey estimates involved in this representation ...
Alberto Lastra +2 more
wiley +1 more source
Eigenfunction expansions of ultradifferentiable functions and ultradistributions [PDF]
, 2016 In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold $X$.
Dasgupta, Aparajita, Ruzhansky, Michael
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Structural theorems for quasiasymptotics of ultradistributions [PDF]
, 2019 We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the origin of ...
Neyt, Lenny, Vindas Diaz, Jasson
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Spectral asymptotics for infinite order pseudo-differential operators [PDF]
, 2018 We study spectral properties of a class of global infinite order pseudo-differential operators and obtain the asymptotic behaviour of the spectral counting functions of such operators.
Pilipović, Stevan +2 more
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