Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms

DOI10.1016/j.jmaa.2016.09.029zbMath1432.35050arXiv1607.04095OpenAlexW2498507845MaRDI QIDQ321849

Chiara Boiti, David Jornet, Alessandro Oliaro

Publication date: 14 October 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.04095

zbMATH Keywords

regularityweighted spacesWigner transformpartial differential operators with polynomial coefficientsSchwartz spaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Transform methods (e.g., integral transforms) applied to PDEs (35A22) General theory of partial differential operators (47F05) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Linear higher-order PDEs (35G05)

Related Items (15)

Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions ⋮ The Wigner global wave front set in spaces of tempered ultradistributions ⋮ Compactness of localization operators on modulation spaces of \(\omega\)-tempered distributions ⋮ The overdetermined Cauchy problem for \(\omega \)-ultradifferentiable functions ⋮ The Gabor wave front set in spaces of ultradifferentiable functions ⋮ Unnamed Item ⋮ Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting ⋮ About the Nuclearity of $$\mathcal {S}_{(M_{p})}$$ and $$\mathcal {S}_{\omega }$$ ⋮ Regularity of global solutions of partial differential equations in non isotropic ultradifferentiable spaces via time-frequency methods ⋮ Real Paley-Wiener theorems in spaces of ultradifferentiable functions ⋮ Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis ⋮ Multipliers on \(\mathcal{S}_{\omega } (\mathbb{R}^N)\) ⋮ Convolutors on \(\mathcal{S}_{\omega}(\mathbb{R}^N)\) ⋮ Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions ⋮ Global wave front sets in ultradifferentiable classes

Cites Work

• The Wigner distribution for classical systems
• Convex analysis and nonlinear optimization. Theory and examples.
• Hermite functions and weighted spaces of generalized functions
• Quasianalytic wave front sets for solutions of linear partial differential operators
• A simple proof of Kotake-Narasimhan theorem in some classes of ultradifferentiable functions
• The overdetermined Cauchy problem for \(\omega \)-ultradifferentiable functions
• Wave front sets with respect to the iterates of an operator with constant coefficients
• Ultradifferentiable functions and Fourier analysis
• Spaces of test functions via the STFT
• Linear partial differential operators and generalized distributions
• Remarks on pseudo-differential operators
• Weyl transforms, the heat kernel and Green function of a degenerate elliptic operator
• Global regularity for ordinary differential operators with polynomial coefficients
• The Weyl Operator and its Generalization
• Characterization for Beurling-Björck space and Schwartz space
• Characterizations of the Gelfand-Shilov spaces via Fourier transforms
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