|
This article is cited in 9 scientific papers (total in 9 papers)
Completeness and minimality of systems of Bessel functions
B. V. Vynnyts'kyi, R. V. Khats' Institute of Physics, Mathematics and Informatics,
Ivan Franko Drohobych State Pedagogical University,
3 Stryiska Str., 82100 Drohobych, Ukraine
Abstract:
We find the necessary and sufficient conditions for the completeness and minimality in the space L2(0;1) of system (√xρkJν(xρk):k∈N) generated by Bessel function of the first kind of index ν⩾−1/2. Moreover, we establish a criterion for the completeness and minimality of system (x−2√xρkJ3/2(xρk):k∈N) in the space L2((0;1);x2dx).
Keywords:
Paley–Wiener theorem, Bessel function, entire function, complete system, minimal system, biorthogonal system, basis.
Received: 30.01.2012
Citation:
B. V. Vynnyts'kyi, R. V. Khats', “Completeness and minimality of systems of Bessel functions”, Ufa Math. J., 5:2 (2013), 131–141
Linking options:
https://www.mathnet.ru/eng/ufa203https://doi.org/10.13108/2013-5-2-131 https://www.mathnet.ru/eng/ufa/v5/i2/p132
|
Statistics & downloads: |
Abstract page: | 1071 | Russian version PDF: | 167 | English version PDF: | 40 | References: | 126 | First page: | 2 |
|