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Approximation par des fonctions holomorphes à croissance contrôlée.

Philippe Charpentier, Yves Dupain, Modi Mounkaila (1994)

Publicacions Matemàtiques

Let Ω be a bounded pseudo-convex domain in Cn with a C∞ boundary, and let S be the set of strictly pseudo-convex points of ∂Ω. In this paper, we study the asymptotic behaviour of holomorphic functions along normals arising from points of S. We extend results obtained by M. Ortel and W. Schneider in the unit disc and those of A. Iordan and Y. Dupain in the unit ball of Cn. We establish the existence of holomorphic functions of given growth having a "prescribed behaviour" in almost all normals arising...

Approximations by the Cauchy-type integrals with piecewise linear densities

Jaroslav Drobek (2012)

Applications of Mathematics

The paper is a contribution to the complex variable boundary element method, shortly CVBEM. It is focused on Jordan regions having piecewise regular boundaries without cusps. Dini continuous densities whose modulus of continuity ω ( · ) satisfies lim sup s 0 ω ( s ) ln 1 s = 0 are considered on these boundaries. Functions satisfying the Hölder condition of order α , 0 < α 1 , belong to them. The statement that any Cauchy-type integral with such a density can be uniformly approximated by a Cauchy-type integral whose density is a piecewise...

Area differences under analytic maps and operators

Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw (2024)

Czechoslovak Mathematical Journal

Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping h and that of z h , we study various L 2 norms for T ϕ ( h ) , where T ϕ is the Toeplitz operator with symbol ϕ . In Theorem , given polynomials p and q we find a symbol ϕ such that T ϕ ( p ) = q . We extend some of our results to the polydisc.

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