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Genkai Zhang 《manuscripta mathematica》1998,97(3):371-388
Let X=G
* be a compact Hermitian symmetric space. We study the Berezin transform on L
2(X) and calculate its spectrum under the decomposition of L
2(X) into the irreducible representations of G
*. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical
line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X.
Received: 10 September 1996 / Revised version: 10 September 1997 相似文献
55.
Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for
the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration
phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper
bounds on spectral gaps.
Received: 10 June 1996 / In revised form: 9 August 1996 相似文献
56.
Hiromichi Kurosu Mizuyo Kikuchi Isao Ando 《Journal of Polymer Science.Polymer Physics》1995,33(5):769-775
The solid-state 15N CP/MAS NMR spectra and 15N spin-lattice relaxation times (T1) of doped and dedoped 15N-labeled polypyrroles prepared by electrochemical polymerization, have been measured by means of high-resolution solid-state 15N NMR. The 15N signal of polypyrrole consists of four peaks decomposed by line shape analysis. The four peaks obtained have been assigned to the various structures of polypyrrole. Further, the half-width of the 15N NMR spectra of polypyrroles is discussed as related to the electrical conductivity. © 1995 John Wiley & Sons, Inc. 相似文献
57.
Marianna A. Shubov 《Integral Equations and Operator Theory》1997,28(3):358-372
We announce a series of results on the spectral analysis for a class of nonselfadjoint opeators, which are the dynamics generators for the systems governed by hyperbolic equations containing dissipative terms. Two such equations are considered: the equation of nonhomogeneous damped string and the 3-dimensional damped wave equation with spacially nonhomogeneous spherically symmetric coefficients. Nonselfadjoint boundary conditions are imposed at the ends of a finite interval or on a sphere centered at the origin respectively. Our main result is the fact the aforementioned operators are spectral in the sense of N. Dunford. The result follows from the fact that the systems of root vectors of the above operators form Riesz bases in the corresponding energy spaces. We also give asymptotics of the spectra and state the Riesz basis property results for the nonselfadjoint operator pencils associated with these operators. 相似文献
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Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4]. 相似文献
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