TL;DR
This paper explores the multiplication properties, functional calculus, and Schatten-von Neumann characteristics of Kato-Sobolev spaces, extending analytical techniques and studying pseudo-differential operators within these spaces.
Contribution
It introduces new multiplication properties, develops an analytic functional calculus, and examines Schatten-von Neumann properties for operators with symbols in Kato-Sobolev spaces.
Findings
Established multiplication properties of Kato-Sobolev spaces
Developed an analytic functional calculus for these spaces
Analyzed Schatten-von Neumann properties of associated pseudo-differential operators
Abstract
We investigate some multiplication properties of Kato-Sobolev spaces by adapting the techniques used in the study of Beurling algebras by Coifman and Meyer. We develop an analytic functional calculus for Kato-Sobolev algebras based on an integral representation formula belonging A. P. Calder\'{o}n. Also we study the Schatten-von Neumann properties of pseudo-differential operators with symbols in the Kato-Sobolev spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Mathematical Physics Problems · Numerical methods in engineering