Geodesic
Iterates of the Bochner--Martinelli Integral Operator in a~Ball
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 137-145.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present paper we prove the convergence of iterates of the integral Bochner–Martinelli operator in a ball in various spaces: the infinitely-smooth functions, the analytic functions and the spaces conjugate to them, the distributions and the analytic functionals. We give a description of a spectrum of this operator in these spaces as well as the space $\mathcal L^p$.
Keywords: Bochner–Martinelli integral operator, iterates. 
@article{JSFU_2009_2_2_a1,
     author = {Alexander M. Kytmanov and Simona G. Myslivets},
     title = {Iterates of the {Bochner--Martinelli} {Integral} {Operator} in {a~Ball}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {137--145},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a1/}
}
TY  - JOUR
AU  - Alexander M. Kytmanov
AU  - Simona G. Myslivets
TI  - Iterates of the Bochner--Martinelli Integral Operator in a~Ball
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2009
SP  - 137
EP  - 145
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a1/
LA  - en
ID  - JSFU_2009_2_2_a1
ER  - 
%0 Journal Article
%A Alexander M. Kytmanov
%A Simona G. Myslivets
%T Iterates of the Bochner--Martinelli Integral Operator in a~Ball
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2009
%P 137-145
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a1/
%G en
%F JSFU_2009_2_2_a1
Alexander M. Kytmanov; Simona G. Myslivets. Iterates of the Bochner--Martinelli Integral Operator in a~Ball. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 137-145. http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a1/

[1] A. V. Romanov, “Spectral analysis of the Bochner–Martinelli operator for the ball in $\mathbb C^n$ and its applications”, Functional Anal. Appl., 12 (1978), 232–234 | DOI | MR

[2] A. V. Romanov, “Convergence of iterates of the Bochner–Martinelli operator and the Cauchy-Riemann equation”, Soviet Math. Dokl., 19:5 (1978), 1211–1215 | Zbl

[3] A. M. Kytmanov, The Bochner–Martinelli integral and its applications, Birkhäuser Verlag, Basel–Boston–Berlin, 1995 | MR | Zbl

[4] Yu. V. Egorov, M. A. Shubin, Partial differential. I. Foundations of the classical theory, Encyclopaedia of Mathematical Sciences, 30, Springer-Verlag, Berlin, 1992 | MR | Zbl

[5] G. M. Henkin, “The method of integral representations in complex analysis”, Several Complex Variables, I, Encyclopaedia of Mathematical Sciences, 7, Springer-Verlag, 1990, 19–116

[6] E. L. Straube, “Harmonic and analytic functions admitting a distribution boundary value”, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 11:4 (1984), 559–591 | MR | Zbl

[7] L. Hörmander, The analysis of linear partial differential operators, I, Springer Verlag, Berlin–Heidelberg–New York–Tokyo, 1983

[8] M. Brelot, Elements de la theorie classique du potential, Paris, 1969

[9] S. L. Sobolev, Introduction to the theory of cubature formulas, Gordon and Breach, Philadelphia, 1992 | MR | Zbl

[10] C. O. Kiselman, “Prolongment des solutions”, Bull. Soc. Math., 97:4 (1965), 345–355

[11] E. M. Stein, Boundary behaviour of holomorphic functions of several complex variables, Princeton Univ. Press, Princeton, NJ, 1972 | MR | Zbl

[12] G. M. Khenkin, E. M. Chirka, “Boundary properties of holomorphic functions of several complex variables”, J. Soviet Math., 5:5 (1976), 612–687 | DOI | Zbl

[13] A. A. Shlapunov, N. N. Tarkhanov, “On the Cauchy problem for holomorphic functions of Lebesgue class $\mathcal L^2$ in a domain”, Sib. Mat. Zh., 33:5 (1992), 186–195 (in Russian) | MR | Zbl

[14] A. M. Kytmanov, S. G. Myslivets, “On Asymptotic Expansion of the Conormal Symbol of the Singular Bochner–Martinelli Operator on the Surfaces with Singular Points”, J Sib. Fed. Univ. Mathematics and Physics, 1:1 (2008), 3–12 | MR