arXiv subjects

S. Thangavelu

Publications and source records attributed to S. Thangavelu.

23 records · Page 2Linked to original sources

arXiv2007

Probabilistic Representations of Solutions of the Forward Equations

In this paper we prove a stochastic representation for solutions of the evolution equation $ \partial_t ψ_t = {1/2}L^*ψ_t $ where $ L^* $ is the formal adjoint of an elliptic second order differential operator with smooth coefficients corresponding to the infinitesimal generator of a finite dimensional diffusion $ (X_t).$ Given $ ψ_0 = ψ$, a distribution with compact support, this representation has the form $ ψ_t = E(Y_t(ψ))$ where the process $ (Y_t(ψ))$ is the solution of a stochastic partial differential equation connected with the stochastic differential equation for $ (X_t) $ via Ito's formula.

math.PR↗

arXiv2007

Holomorphic Sobolev spaces associated to compact symmetric spaces

Using Gutzmer's formula, due to Lassalle, we characterise the image of Sobolev spaces under the Segal-Bargmann transform on compact Riemannian symmetric spaces.

math.FA↗

arXiv2007

An analogue of Gutzmer's formula for Hermite expansions

We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of $ L^2(\R^n) $ under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.

math.CA↗

arXiv2007

Heat kernel transform for nilmanifolds associated to the Heisenberg group

We study the heat kernel transform on a nilmanifold $ M $ of the Heisenberg group. We show that the image of $ L^2(M) $ under this transform is a direct sum of weighted Bergman spaces which are related to twisted Bergman and Hermite-Bergman spaces.

math.FA↗

arXiv2003

Probabilistic representations of solutions to the heat equation

In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $ϕ$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition $ϕ$, is given by the convolution of $ϕ$ with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation to initial conditions that are arbitrary tempered distributions.

math.PR↗