Abstract
S. Abbott and B. Hanson developed an
operator-theoretic approach to solve some extremal problems. We give
a different proof of a theorem of S. Abbott and B. Hanson in the
case when the corresponding operator is unbounded. We apply our
theorem to the classical Kolmogorov and Szegö infimum problems.
We also consider Kolmogorov and Szegö type infima, when
integration over the unit circle is replaced by integration over the
unit disk.
С. Аббот і Б. Хенсон розвинули теоретико-операторний підхід
до розв’язанні деяких екстремальних задач. Ми даємо нове доведення
теореми С. Аббота і Б. Хенсона для випадку, коли відповідний
оператор необмежений. Теорема застосовується для класичних задач
Колмогорова і Сеге про інфімум. Також розглянуті задачі Колмогорова
і Сеге про інфімум для випадку, коли інтегрування ведеться не по
колу, а по кругу.
Key words: Unbounded operator, Kolmogorov infimum, Szegö infimum, Hardy space, Bergman space.
Full Text
Article Information
| Title | An Operator Approach to Extremal Problems on Hardy and Bergman Spaces |
| Source | Methods Funct. Anal. Topology, Vol. 27 (2021), no. 2, 142-150 |
| DOI | 10.31392/MFAT-npu26_2.2021.02 |
| MathSciNet |
MR4296403 |
| Milestones | Received 26/07/2020; Revised 12/03/2021 |
| Copyright | The Author(s) 2021 (CC BY-SA) |
Authors Information
Miron B. Bekker
Department of Mathematics the University of Pittsburgh at Johnstown, 450 Schoolhouse Rd, Johnstown PA 15904
Joseph A. Cima
Department of Mathematics The University of North Carolina at Chapel Hill, CB 3250, 329 Phillips Hall, Chapel Hill, NC 27599
Citation Example
Miron B. Bekker and Joseph A. Cima, An Operator Approach to Extremal Problems on Hardy and Bergman Spaces, Methods Funct. Anal. Topology 27
(2021), no. 2, 142-150.
BibTex
@article {MFAT1560,
AUTHOR = {Miron B. Bekker and Joseph A. Cima},
TITLE = {An Operator Approach to Extremal Problems on Hardy and Bergman Spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {27},
YEAR = {2021},
NUMBER = {2},
PAGES = {142-150},
ISSN = {1029-3531},
MRNUMBER = {MR4296403},
DOI = {10.31392/MFAT-npu26_2.2021.02},
URL = {http://mfat.imath.kiev.ua/article/?id=1560},
}
