A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

• Autorzy: A. Perälä , J. A. Virtanen , L. Wolf
• Języki publikacji: EN

Abstrakty

EN

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

Słowa kluczowe

EN

Riemann-Hilbert problems; Hardy spaces; Toeplitz operators; Fredholm properties; eigenvalues

Kategorie tematyczne

• 35Q15: Riemann-Hilbert problems
• 45E05: Integral equations with kernels of Cauchy type
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
• 30E25: Boundary value problems

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2013
• Tom: 1
• Strony: 28-36

Daty

otrzymano

2013-05-28

zaakceptowano

2013-08-06

online

2013-09-16

Twórcy

autor

A. Perälä

• Department of Mathematics, University of Helsinki,
  Helsinki 00014, Finland,

autor

J. A. Virtanen

• Department of Mathematics, University of Reading,
  Whiteknights, P.O. Box 220, Reading RG6 6AX, U.K.,

autor

L. Wolf

• Department of Mathematics and Statistics,
  State University of New York at Albany, Albany, N.Y. 12222, U.S.A.,

Bibliografia

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Identyfikatory

DOI

10.2478/conop-2012-0004