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A multidimensional analogue of a formula of Carleman. (English. Russian original) Zbl 0586.32005

Sov. Math., Dokl. 30, 241-244 (1984); translation from Dokl. Akad. Nauk SSSR 277, 1289-1291 (1984).
This paper concerns a further extension of the classical integral formula by T. Carleman [Les fonctions quasi analytiques. Paris: Gauthier-Villars (1926; JFM 52.0255.02)] for holomorphic functions, beyond the works of G. M. Goluzin (misspelled in the text) and V. I. Krylov [Rec. Math. Moscou 40, 144–149 (1933; Zbl 0007.41601)], D. J. Patil [Trans. Am. Math. Soc. 188, 97–103 (1974; Zbl 0243.32006)] and others. A main motivation and interest in this problem stems from ill-posed and conditionally well-posed problems (in the sense of M. M. Lavrent’ev).

MSC:

32A40 Boundary behavior of holomorphic functions of several complex variables
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32D99 Analytic continuation
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
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