Approximation of holomorphic mappings on strongly pseudoconvex domains

Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We prove that the set A(D,Y), consisting of all continuous maps from the closure of D to Y which are holomorphic in D, is a complex Banach manifold. When D is the unit disc in C (or any other topologically trivial strongly pseudoconvex domain in a Stein manifold), A(D,Y) is locally modeled on the Banach space A(D,C^n)=A(D)^n with n=dim Y. Analogous results hold for maps which are holomorphic in D and of class C^r up to the boundary for any positive integer r. We also establish the Oka property for sections of continuous or smooth fiber bundles over the closure of D which are holomorphic over D and whose fiber enjoys the Convex approximation property. The main analytic technique used in the paper is a method of gluing holomorphic sprays over Cartan pairs in Stein manifolds, with control up to the boundary, which was developed in our paper "Holomorphic curves in complex manifolds" (Duke Math. J. 139 (2007), no. 2, 203--253)

Analysis of the application of the optical method to the measurements of the water vapor content in the atmosphere - Part 1: Basic concepts of the measurement technique

We retrieved the total content of the atmospheric water vapor (or Integrated Water Vapor, IWV) from extensive sets of photometric data obtained since 1995 at Lindenberg Meteorological Observatory with star and sun photometers. Different methods of determination of the empirical parameters that are necessary for the retrieval are discussed. The instruments were independently calibrated using laboratory measurements made at Pulkovo Observatory with the VKM-100 multi-pass vacuum cell. The empirical parameters were also calculated by the simulation of the atmospheric absorption by water vapor, using the MODRAN-4 program package for different model atmospheres. The results are compared to those presented in the literature, obtained with different instruments and methods of the retrieval. The reliability of the empirical parameters, used for the power approximation that links the water vapor content with the observed absorption, is analyzed. Currently, the total (from measurements, calibration, and calculations) errors yield the standard uncertainty of about 10% in the total column water vapor. We discuss the possibilities for improving the accuracy of calibration to ~1% as indispensable condition in order to make it possible to use data obtained by optical photometry as an independent reference for other methods (GPS, MW-radiometers, lidar, etc).Comment: 28 pages, 8 figures, 3 tables. In submitting to Atmospheric Measurement Technique