Published December 18, 2008
| public
Book Section - Chapter
Some Problems Concerning the Test Functions in the Szegö and Avram-Parter Theorems
Abstract
The Szegö and Avram-Parter theorems give the limit of the arithmetic mean of the values of certain test functions at the eigenvalues and singular values of Toeplitz matrices as the matrix dimension increases to infinity. This paper is concerned with some questions that arise when the test functions do not satisfy the known growth restrictions at infinity or when the test function has a logarithmic singularity within the range of the symbol. Several open problems are listed and accompanied by a few new results that illustrate the delicacy of the matter.
Additional Information
© 2008 Birkhäuser Verlag Basel/Switzerland. The second author was partially supported by CONACYT project U46936-F, Mexico.Additional details
- Eprint ID
- 102060
- DOI
- 10.1007/978-3-7643-8893-5_3
- Resolver ID
- CaltechAUTHORS:20200323-145009694
- U46936-F
- Consejo Nacional de Ciencia y Tecnología (CONACYT)
- Created
-
2020-03-23Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Series Name
- Operator Theory: Advances and Applications
- Series Volume or Issue Number
- 187