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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.

Associated weights and spaces of holomorphic functions

Klaus Bierstedt, José Bonet, Jari Taskinen (1998)

Studia Mathematica

When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset G N which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize...

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