Asymptotic Analysis of Symmetric Functions

The Asymptotic Expansion of Spherical Functions on Symmetric Cones

In [7], Genkai Zhang gives the asymptotic expansion for the spherical functions on symmetric cones. This is done to prove a central limit theorem for these spaces. The work of Zhang is a natural continuation of the work of Audrey Terras [6] (the case of the positive definite matrices of rank 2) and of the work of Donald St.P. Richards [3] (the case of the positive definite matrices of all ranks...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Qualitative Asymptotic Analysis of Complex Functions

Professional scientists and engineers frequently analyze problems with heuristic techniques to get crude solutions quickly without worrying about the details of mathematical justification and firm error estimates. The method of steepest descent is one such technique that is widely used to evaluate functions represented by complex integrals. Routine application of the method however requires the...

Non-asymptotic Analysis of Bandlimited Functions

physics (e.g. wave phenomena, fluid dynamics) to engineering (e.g. signal processing, filter design). Even though the significance of PSWFs was realized at least half a century ago, and they frequently occur in applications, their analytical properties have not been investigated as much as those of many other special functions. In particular, despite some recent progress, the gap between asympt...

Asymptotic Analysis of Non-symmetric Linear Operators via Γ-convergence

We study the asymptotic behavior of a sequence of Dirichlet problems for second order linear operators in divergence form { −div(σε∇u) = f in Ω, u ∈ H1 0 (Ω), where (σε) ⊂ L∞(Ω;Rn×n) is uniformly elliptic and possibly non-symmetric. On account of the variational principle of Cherkaev and Gibiansky [1], we are able to prove a variational characterization of the H-convergence of (σε) in terms of ...