SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE

doi:10.1007/s10473-020-0609-4

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1739-1752.doi: 10.1007/s10473-020-0609-4

SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE

M. O. AGWANG, J. O. BONYO

Department of Pure and Applied Mathematics, Maseno University, P. O. BOX 333-40105, Maseno, Kenya

收稿日期:2019-07-18 修回日期:2020-03-14 出版日期:2020-12-25 发布日期:2020-12-30
通讯作者: J. O. BONYO,E-mail:jobbonyo@maseno.ac.ke E-mail:jobbonyo@maseno.ac.ke
作者简介:M. O. AGWANG,E-mail:omeshackagwang@yahoo.com
基金资助:
This work was partially supported by a grant from the Simons Foundation.

SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE

M. O. AGWANG, J. O. BONYO

Department of Pure and Applied Mathematics, Maseno University, P. O. BOX 333-40105, Maseno, Kenya

Received:2019-07-18 Revised:2020-03-14 Online:2020-12-25 Published:2020-12-30
Contact: J. O. BONYO,E-mail:jobbonyo@maseno.ac.ke E-mail:jobbonyo@maseno.ac.ke
Supported by:
This work was partially supported by a grant from the Simons Foundation.

摘要/Abstract

摘要： We prove that the group of weighted composition operators induced by continuous automorphism groups of the upper half plane $\mathbb{U}$ is strongly continuous on the weighted Dirichlet space of $\mathbb{U}$, $\mathcal{D}_{α}$($\mathbb{U}$). Further, we investigate when they are isometries on $\mathcal{D}_{α}$($\mathbb{U}$). In each case, we determine the semigroup properties while in the case that the induced composition group is an isometry, we apply similarity theory to determine the spectral properties of the group.

关键词: one-parameter semigroup, composition operator semigroups, strong continuity, infinitesimal generator, spectra

Abstract: We prove that the group of weighted composition operators induced by continuous automorphism groups of the upper half plane $\mathbb{U}$ is strongly continuous on the weighted Dirichlet space of $\mathbb{U}$, $\mathcal{D}_{α}$($\mathbb{U}$). Further, we investigate when they are isometries on $\mathcal{D}_{α}$($\mathbb{U}$). In each case, we determine the semigroup properties while in the case that the induced composition group is an isometry, we apply similarity theory to determine the spectral properties of the group.

Key words: one-parameter semigroup, composition operator semigroups, strong continuity, infinitesimal generator, spectra

中图分类号:

47B38

M. O. AGWANG, J. O. BONYO. SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE[J]. 数学物理学报(英文版), 2020, 40(6): 1739-1752.

M. O. AGWANG, J. O. BONYO. SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE[J]. Acta mathematica scientia,Series B, 2020, 40(6): 1739-1752.

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SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE

SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE

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