Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles

In this paper we study the asymptotic behaviour of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. This implies a full asymptotic expansion of this function on the set where the curvature of the line bundle is non-degenerate. As application we obtain the Bergman kernel asymptotics for adjoint semi-positive line bundles over complete Kaehler manifolds, on the set where the curvature is positive. We also prove the asymptotics for big line bundles endowed with singular Hermitian metrics with strictly positive curvature current. In this case the full asymptotics holds outside the singular locus of the metric.Comment: 71 pages; v.2 is a final update to agree with the published pape

On the stability of equivariant embedding of compact CR manifolds with circle action

We prove the stability of the equivariant embedding of compact strictly pseudoconvex CR manifolds with transversal CR circle action under circle invariant perturbations of the CR structures.Comment: 21 pages, final versio

Time-Dependent Fluid-Structure Interaction

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to as a fluid-structure interaction and is mathematically formulated as a time-dependent transmission problem. In this paper, we consider a typical fluid-structure interaction problem by using a coupling procedure which reduces the problem to a nonlocal initial-boundary problem in the elastic body with a system of integral equations on the interface between the domains occupied by the elastic body and the fluid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform, an essential feature of which is that it works directly on data in the time domain rather than in the transformed domain. Our results may serve as a mathematical foundation for treating time-dependent fluid-structure interaction problems by convolution quadrature coupling of FEM and BEM

Design and applications of a graphics package for the HP1000 computer.

The objective of this thesis is to develop the FORTRAN subroutine PLOTER which is a general-purpose plotting tool to plot charts on a Hewlett Packard plotter. The programs RESP and INVLAP which can plot the frequency and time responses of system functions are modified to adopt the PLOTER subroutine and are stored of the HP1000-A900 minicomputer whose software, the GRAPHICS/1000, supports the graphics ability of PLOTER. This thesis describes the theories, functions, software techniques and operations of the PLOTER subroutine and the application programs RESP and the INVLAP. It also provides program listings and example plots

Semi-classical spectral asymptotics of Toeplitz operators on strictly pseudodonvex domains

On a relatively compact strictly pseudoconvex domain with smooth boundary in a complex manifold of dimension $n$ we consider a Toeplitz operator $T_R$ with symbol a Reeb-like vector field $R$ near the boundary. We show that the kernel of a weighted spectral projection $\chi(k^{-1}T_R)$, where $\chi$ is a cut-off function with compact support in the positive real line, is a semi-classical Fourier integral operator with complex phase, hence admits a full asymptotic expansion as $k\to+\infty$. More precisely, the restriction to the diagonal $\chi(k^{-1}T_R)(x,x)$ decays at the rate $O(k^{-\infty})$ in the interior and has an asymptotic expansion on the boundary with leading term of order $k^{n+1}$ expressed in terms of the Levi form and the pairing of the contact form with the vector field $R$.Comment: 17 page