Results 1 to 10 of about 125 (119)
Local Hypoellipticity by Lyapunov Function
Abstract and Applied Analysis, 2016 We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: Lj=∂/∂tj+(∂ϕ/∂tj)(t,A)A, j=1,2,…,n, where A:D(A)⊂H→H is a self-adjoint linear ...
E. R. Aragão-Costa
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Hypoellipticity and Non Hypoellipticity for Sums of Squares of Complex Vector Fields
Bruno Pini Mathematical Analysis Seminar, 2011 In this talk we give a report on a paper where we consider a model sum of squares of planar complex vector fields, being close to Kohn's operator but with a point singularity.
Antonio Bove
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Graded hypoellipticity of BGG sequences. [PDF]
Ann Glob Anal Geom (Dordr), 2022 AbstractThis article studies hypoellipticity on general filtered manifolds. We extend the Rockland criterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix and describe its precise analytic structure. We use this result to study Rockland sequences, a notion generalizing elliptic sequences to filtered manifolds.
Dave S, Haller S.
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On the regularity of the solutions and of analytic vectors for “sums of squares”
Bruno Pini Mathematical Analysis Seminar, 2023 We present a brief survey on some recent results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of H"ormander type.
Gregorio Chinni
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On differential operators an differential equations on torus
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2018 In this paper, we consider periodic boundary value problems for a differential equation whose coefficients are trigonometric polynomials. The spaces of generalized functions are constructed, in which the problems considered have solutions, in particular,
Vladimir P Burskii
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Analytic Hypoellipticity and the Treves Conjecture
Bruno Pini Mathematical Analysis Seminar, 2016 We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic
Marco Mughetti
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Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Abstract and Applied Analysis, 2013 General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties
Mawardi Bahri +2 more
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Some advances in analytic hypoellipticity
Bruno Pini Mathematical Analysis SeminarWe present a brief survey on the theory of the real analytic regularity for the solutions to sums of squares of vector fields satisfying the Hörmander condition.
Marco Mughetti
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Pseudodifferential operators with generalized symbols and regularity theory
Electronic Journal of Differential Equations, 2005 We study pseudodifferential operators with amplitudes $a_varepsilon (x,xi)$ depending on a singular parameter $varepsilon o 0$ with asymptotic properties measured by different scales.
Claudia Garetto +2 more
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Elliptic regularity and solvability for partial differential equations with Colombeau coefficients
Electronic Journal of Differential Equations, 2004 This paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau.
Gunther Hormann +1 more
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