A theorem of Strichartz for multipliers on homogeneous trees

Autor:	Rano, Sumit Kumar, Sarkar, Rudra P.
Rok vydání:	2024
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis Primary 43A85 Secondary 20E08 39A12 43A90
Druh dokumentu:	Working Paper
Popis:	A theorem of Strichartz states that if a uniformly bounded bi-infinite sequence of functions on the Euclidean spaces, satisfies the condition that the Laplacian acting on a function in this sequence yields the next one, then each function in this sequence is an eigenfunction of the Laplacian. We consider a generalization of this result for homogeneous trees, where we replace bounded functions by tempered distributions and the Laplacian by multiplier operators acting on the tempered distributions. After establishing the result in this general context, we narrow our focus to specific cases, which includes important examples of multiplier operators such as heat and Schr\"odinger operator, ball and sphere averages of function. Comment: 32 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.10703 Zobrazit plný text záznamu View this record from Arxiv