Wave Front Sets and Regularity for Fourier Integral Operators with Symbols in Anisotropic Sobolev Spaces Article Swipe
Revista, Zen
,
MATH, 10
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17830023
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17830023
This paper investigates the regularity properties of Fourier integral operators (FIOs) when their symbols belong to anisotropic Sobolev spaces. We establish precise connections between the wave front sets of distributions and the mapping properties of these operators. Specifically, we analyze how the anisotropic nature of the symbol affects the propagation of singularities. The study combines microlocal analysis techniques with the theory of anisotropic Sobolev spaces to provide sharp estimates for the regularity of solutions to pseudodifferential equations. Furthermore, we explore applications to the Cauchy problem for hyperbolic partial differential equations with variable coefficients, demonstrating the utility of our results in characterizing the smoothness of solutions.
Related Topics
Concepts
Sobolev space
Microlocal analysis
Mathematics
Smoothness
Fourier integral operator
Fourier transform
Mathematical analysis
Anisotropy
Partial differential equation
Variable (mathematics)
Fourier analysis
Continuation
Modulation space
Pure mathematics
Dimension (graph theory)
Cauchy distribution
Fourier series
Operator theory
Cauchy problem
Front (military)
Sobolev inequality
Differential operator
Reflection (computer programming)
Partial derivative
Pseudodifferential operators
Lp space
Section (typography)
Domain (mathematical analysis)
Initial value problem
Interpolation space
Differential (mechanical device)
Wavefront
Hyperbolic partial differential equation
Interval (graph theory)
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17830023
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7108907643
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W7108907643Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17830023Digital Object Identifier
- Title
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Wave Front Sets and Regularity for Fourier Integral Operators with Symbols in Anisotropic Sobolev SpacesWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
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2025-12-05Full publication date if available
- Authors
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Revista, Zen, MATH, 10List of authors in order
- Landing page
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https://doi.org/10.5281/zenodo.17830023Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://doi.org/10.5281/zenodo.17830023Direct OA link when available
- Concepts
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Sobolev space, Microlocal analysis, Mathematics, Smoothness, Fourier integral operator, Fourier transform, Mathematical analysis, Anisotropy, Partial differential equation, Variable (mathematics), Fourier analysis, Continuation, Modulation space, Pure mathematics, Dimension (graph theory), Cauchy distribution, Fourier series, Operator theory, Cauchy problem, Front (military), Sobolev inequality, Differential operator, Reflection (computer programming), Partial derivative, Pseudodifferential operators, Lp space, Section (typography), Domain (mathematical analysis), Initial value problem, Interpolation space, Differential (mechanical device), Wavefront, Hyperbolic partial differential equation, Interval (graph theory)Top concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| abstract_inverted_index.solutions | 73 |
| abstract_inverted_index.equations. | 76 |
| abstract_inverted_index.hyperbolic | 86 |
| abstract_inverted_index.microlocal | 55 |
| abstract_inverted_index.operators. | 36 |
| abstract_inverted_index.properties | 5, 33 |
| abstract_inverted_index.regularity | 4, 71 |
| abstract_inverted_index.smoothness | 102 |
| abstract_inverted_index.solutions. | 104 |
| abstract_inverted_index.techniques | 57 |
| abstract_inverted_index.anisotropic | 16, 42, 62 |
| abstract_inverted_index.connections | 22 |
| abstract_inverted_index.propagation | 49 |
| abstract_inverted_index.Furthermore, | 77 |
| abstract_inverted_index.applications | 80 |
| abstract_inverted_index.differential | 88 |
| abstract_inverted_index.investigates | 2 |
| abstract_inverted_index.Specifically, | 37 |
| abstract_inverted_index.coefficients, | 92 |
| abstract_inverted_index.demonstrating | 93 |
| abstract_inverted_index.distributions | 29 |
| abstract_inverted_index.characterizing | 100 |
| abstract_inverted_index.singularities. | 51 |
| abstract_inverted_index.pseudodifferential | 75 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.88507385 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |