Characterization of eigenfunctions of the Laplace-Beltrami operator through radial averages on rank one symmetric spaces/ Muna Naik
Material type:
- 23rd. 516.362 M963
- Guided by Prof. Rudra Sarkar
Item type | Current library | Call number | Status | Notes | Date due | Barcode | Item holds | |
---|---|---|---|---|---|---|---|---|
THESIS | ISI Library, Kolkata | 516.362 M963 (Browse shelf(Opens below)) | Available | E-Thesis | TH486 |
Browsing ISI Library, Kolkata shelves Close shelf browser (Hides shelf browser)
Thesis (Ph.D.) - Indian Statistical Institute, 2019
Preliminaries -- Characterization of eigenfunctions from the equation f ∗ µ = f -- Characterization of eigenfunctions via Roe–Strichartz type theorems -- Mean value property in limit, a result of Plancherel–P´olya and Benyamini–Weit -- Large and small time behaviour of heat propagation
Guided by Prof. Rudra Sarkar
Let X be a rank one Riemannian symmetric space of noncompact type and ∆
be the Laplace–Beltrami operator of X. The space X can be identified with the
quotient space G/K where G is a connected noncompact semisimple Lie group of real rank one with finite centre and K is a maximal compact subgroup of G. Thus G acts naturally on X by left translations. Through this identification, a function or measure on X is radial (i.e. depends only on the distance from eK), when it is invariant under the left-action of K. We consider right-convolution operators Θ on functions f on X defined by, Θ : f 7→ f ∗ µ where µ is a radial (possibly complex) measure on X. These operators will be called multipliers. In particular Θ is a radial average when µ is a radial probability measure. Notable examples of radial averages are ball, sphere and annular averages. Another well known example is f 7→ f ∗ ht, where ht is the heat kernel on X. This will be called heat propagator and will be denoted by e t∆. In this thesis we shall study the questions of the following genre. Below by eigenfunction we mean eigenfunction of ∆.
There are no comments on this title.