Steven G. Krantz

A Primer of Real Analytic Functions

Preface to the Second Edition * Preface to the First Edition * Elementary Properties * Multivariable Calculus of Real Analytic Functions * Classical Topics * Some Questions of Hard Analysis * Results Motivated by Partial Differential Equations * Topics in Geometry * Bibliography * Index

Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary

A rigidity theorem for holomorphic mappings, in the nature of the uniqueness statement of the classical one-variable Schwarz lemma, is proved at the boundary of a strongly pseudoconvex domain. The result reduces to an interesting, and apparently new, result even in one complex dimension. The theorem has a variety of geometric and analytic interpretations. DEPARTMENT OF MATHEMATICS, UNIVERSITY OF MICHIGAN, ANN ARBOR, MICHIGAN 48109 DEPARTMENT OF MATHEMATICS, Box 1146, WASHINGTON UNIVERSITY IN ST. LOUIS, ST. LOUIS, MISSOURI 63130 This content downloaded from 40.77.167.14 on Wed, 15 Jun 2016 05:36:04 UTC All use subject to http://about.jstor.org/terms

Deformation of complex structures, estimates for the ∂ equation, and stability of the Bergman kernel

The purpose of this paper is to investigate the stability, under perturbation of the boundary or ,of the complex structure, of the solutions to the

Analysis designs, and behavior of dissipative joints for coupled beams

Neumann problem on smoothly bounded strongly pseudoconvex domains and of the Fefferman asymptotic expansion of the Bergman kernel on these domains. The significance of these results arises in part from the fact that there is little hope of realizing the Bergman kernel explicitly except in the restricted case of homogeneous domains. Since a homogeneous C”O strongly pseudoconvex domain is necessarily biholomorphic to the ball, it is thus only through general results, such as the asymptotic expansion, that the Bergman kernels of strongly pseudoconvex domains not biholomorphic to the ball can be studied. The stability of the Bergman kernel has two aspects:. (i) Stability of behavior in the region where the kernel is C”O and bounded (i.e., pairs of points which are away from the boundary or from each other) and (ii) stability in the region consisting of pairs of points simultaneously near the boundary and near each other, where the kernel becomes unbounded as the boundary is approached. Specifically if D is a C” strongly pseudoconvex domain in C” and if E, = {(z, w) E b x 6: ] z w ( + dis(z, aD) + dis(w, 80) < S}, then the Bergman kernel function K,: D X D + Cc is CW on D x DIE, for any positive 6 [37]. Here it will be shown (Theorem 3.38) that for fixed 6 > 0, the Cw function KD ]orXWII varies continuously in the C” topology. This result is established using a stability result (Theorem 3.10) for the &Neumann operator which states in effect that P small perturbations of the complex structure of a fixed domain result in a small perturbation of the Neumann operator for the Cauchy-Riemann complex which is small in

Distance to Ck hypersurfaces

In the construction of modern large flexible space structures, active and passive damping devices are commonly installed at joints of coupled beams to achieve the suppression of vibration. In order to successfully control such dynamic structures, the function and behavior of dissipative joints must be carefully studied.These dissipative joints are analyzed by first classifying them into types according to the discontinuities of physical variables across a joint. The four important physical variables for beams are displacement

Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, II

( y )

The geometry of complex domains

, rotation

A criterion for normality in Cn

( \theta )

On a problem of Moser

, bending moment

The Schwarz lemma at the boundary

( M )