Abstract
We present an exact inner structure of the block Jacobi type matrix
related to the complex moment problem with the corresponding
measure supported on an arbitrary second order curve in the complex
plane. For completeness of the study we also present a solution of
the direct and inverse spectral problems for such matrices. In this
the way, we give a necessary and sufficient condition under which a
matrix in the CMV-form generates a (pre)normal operator, namely, not
obligatory a unitary one.
Надано точну внутрішню структуру блочної якоюієвої матриці,
яка пов'язана з комплексною проблемою моментів і мірою, що міє носій
на довільній кривій другого порядку в комплексній площині. Для
повноти дослідження подаємо також розв'язок прямої та оберненої
спектральних задачі для таких матриць. Ми також даємо необхідну і
достатню умову зв якої CMV-матриця породжує (пре)нормальний
оператор, а саме не обов'язково унітарний.
Key words: Trigonometric, complex, Hamburger, classic, strong moment problem,
Jacobi type three-diagonal matrix, CMV-matrix
Full Text
Article Information
| Title | The inner structure of the block Jacobi type matrix related
to the complex moment problem with
the measure supported on the second order curve |
| Source | Methods Funct. Anal. Topology, Vol. 28 (2022), no. 3, 209-227 |
| DOI | 10.31392/MFAT-npu26_3.2022.02 |
| MathSciNet |
MR4550659 |
| Milestones | Received 25/08/2022; Revised 09/09/2022 |
| Copyright | The Author(s) 2022 (CC BY-SA) |
Authors Information
Mykola Dudkin
Department of Physic and Mathematics, I. Sikorsky Kyiv Polytechnic Institute, National Technical University of Ukraine, Kyiv, Ukraine
Olga Dyuzhenkova
Department of Physic and Mathematics, I. Sikorsky Kyiv Polytechnic Institute, National Technical University of Ukraine, Kyiv, Ukraine
Valentyna Kozak
Department of Physic and Mathematics, I. Sikorsky Kyiv Polytechnic Institute, National Technical University of Ukraine, Kyiv, Ukraine
Citation Example
Mykola Dudkin, Olga Dyuzhenkova, and Valentyna Kozak, The inner structure of the block Jacobi type matrix related
to the complex moment problem with
the measure supported on the second order curve, Methods Funct. Anal. Topology 28
(2022), no. 3, 209-227.
BibTex
@article {MFAT1795,
AUTHOR = {Mykola Dudkin and Olga Dyuzhenkova and Valentyna Kozak},
TITLE = {The inner structure of the block Jacobi type matrix related
to the complex moment problem with
the measure supported on the second order curve},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {28},
YEAR = {2022},
NUMBER = {3},
PAGES = {209-227},
ISSN = {1029-3531},
MRNUMBER = {MR4550659},
DOI = {10.31392/MFAT-npu26_3.2022.02},
URL = {http://mfat.imath.kiev.ua/article/?id=1795},
}
