Volterra operators in the edge-calculus
- We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained byWe study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).…
Author details: | Der-Chen ChangGND, Mahdi Hedayat MahmoudiORCiD, Bert-Wolfgang SchulzeGND |
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DOI: | https://doi.org/10.1007/s13324-018-0238-4 |
ISSN: | 1664-2368 |
ISSN: | 1664-235X |
Title of parent work (English): | Analysis and Mathematical Physics |
Publisher: | Springer |
Place of publishing: | Basel |
Publication type: | Article |
Language: | English |
Date of first publication: | 2018/06/19 |
Publication year: | 2018 |
Release date: | 2021/07/05 |
Tag: | Anisotropic pseudo-differential operators; Edge calculus; Operator-valued symbols of Mellin type; Volterra operator |
Volume: | 8 |
Issue: | 4 |
Number of pages: | 20 |
First page: | 551 |
Last Page: | 570 |
Funding institution: | NSFNational Science Foundation (NSF) [DMS-1408839]; McDevitt Endowment Fund at Georgetown University |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |