We consider Steklov eigenvalues of three-dimensional, nearly-spherical domains. In previous work, we have shown that the are analytic functions domain perturbation parameter. Here, compute first-order term asymptotic expansion, which can explicitly be written in terms Wigner 3-jsymbols. analyze expansion and prove isoperimetric result that, if l is a square integer, volume-normalized l-th eigen...

This paper investigates the stability properties of spectrum classical Steklov problem under domain perturbation. We find conditions which guarantee spectral and we show their optimality. emphasize fact that our results also involve convergence eigenfunctions in a suitable sense according with definition connecting system by Vainikko (1979). The can be expressed terms H1 strong convergence. arg...

In this note, we find a sharp upper bound for the Steklov spectrum on submanifold of revolution in Euclidean space with one boundary component.

Coherent states on the quantum group SUq(2) are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit q → 1 is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to q-deformation as a q-Weyl quantization and a relavence of co...

Let Xt be a Cauchy process in R, d ≥ 1. We investigate some of the fine spectral theoretic properties of the semigroup of this process killed upon leaving a domain D. We establish a connection between the semigroup of this process and a mixed boundary value problem for the Laplacian in one dimension higher, known as the “Mixed Steklov Problem.” Using this we derive a variational characterizatio...

In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian on graphs discuss its rigidity. As applications the eigenvalues, Lichnerowicz-type estimates some combinatorial for graphs.