Pick-Nevanlinna interpolation on finitely-connected domains

• Autorzy: Stephen D. Fisher
• Języki publikacji: EN

Abstrakty

EN

Let Ω be a domain in the complex plane bounded by m+1 disjoint, analytic simple closed curves and let $z_0,...,z_n$ be n+1 distinct points in Ω. We show that for each (n+1)-tuple $(w_0,...,w_n)$ of complex numbers, there is a unique analytic function B such that: (a) B is continuous on the closure of Ω and has constant modulus on each component of the boundary of Ω; (b) B has n or fewer zeros in Ω; and (c) $B(z_j) = w_j$, 0 ≤ j ≤ n.

Kategorie tematyczne

• 30J10: Blaschke products
• 30C99: None of the above, but in this section
• 30E05: Moment problems, interpolation problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 103
• Numer: 3
• Strony: 265-273

Daty

wydano

1992

otrzymano

1992-01-17

Twórcy

autor

Stephen D. Fisher

• Department of Mathematics, Northwestern University, Evanston, Illinois 60208, U.S.A.

Bibliografia

• [A] L. Ahlfors, Conformal Invariants: Topics in Geometric Function Theory, McGraw-Hill, New York 1973.
• [CW] R. Coifman and G. Weiss, A kernel associated with certain multiply connected domains and its application to factorization theorems, Studia Math. 28 (1966), 31-68.
• [D] Ph. Delsarte, Y. Genin and Y. Kamp, The Pick-Nevanlinna problem, Internat. J. Circuit Theory Appl. 9 (1981), 177-187.
• [F] S. D. Fisher, Function Theory on Planar Domains, Wiley, New York 1983.
• [FM1] S. D. Fisher and C. A. Micchelli, n-widths of sets of analytic functions, Duke Math. J. 47 (1980), 789-801.
• [FM2] S. D. Fisher and C. A. Micchelli, Optimal sampling of holomorphic functions II, Math. Ann. 273 (1985), 131-147.
• [G] P. Garabedian, Schwarz's lemma and the Szegö kernel function, Trans. Amer. Math. Soc. 67 (1949), 1-35.
• [M] J. Munkres, Elements of Algebraic Topology, Addison-Wesley, Menlo Park, Calif., 1984.