Product formulas and convolutions for Laplace-Beltrami operators on product spaces: beyond the trivial case

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Sousa, R (Author) Other; Guerra, M (Author) Other; Yakubovich, SB (Author) FCUP

Journal

Title: Mathematische Annalen

Vol. 387

Pages: 879-926

ISSN: 0025-5831

Publisher: Springer Nature

Indexing

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Other information

Authenticus ID: P-00X-7EW

DOI: 10.1007/s00208-022-02424-6

Abstract (EN): We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on product manifolds endowed with warped Riemannian metrics. This structure gives rise to a convolution semigroup representation for the Markovian semigroup generated by the Laplace-Beltrami operator. We provide several examples on the product R+ x T, and include a study of product formulas and convolution structures generated by elliptic operators on R-0(+) x I (I being an interval).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 48