2019/02/05 by Geetanjali M. Phatak, Phatak, Geetanjali M., V. M. Sholapurkar +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Functional Analysis (math.FA) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1902.01708
openalex publication_date 2019/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
M. Embry and A. Lambert initiated the study of a weighted translation semigroup \St\ in \cal B(L2(\mathbb R+)), with a view to explore a continuous analogue of a weighted shift operator. We continued the work, characterized some special types of semigroups and developed an analytic model for the left invertible weighted translation semigroup. The present paper deals with the generalization of the weighted translation semigroup in multi-variable set up. We develop the toral analogue of the analytic model and also describe the spectral picture. We provide many examples of weighted translation semigroups in multi-variable case. Further, we replace the space L2(\mathbb R+) by L2(\mathbb R+d) and explore the properties of weighted translation semigroup \S_t\ in \cal B(L2(\mathbb R+d)), in both one and multi variable cases.