|
|
On derivatives of conjugate trigonometric polynomials in $L_0$ (in Russian) |
| Author |
A. N. Adamov
alex.1985@mail.ru
Îäåññêèé íàöèîíàëüíûé óíèâåðñèòåò ³ì. È.È. Ìå÷íèêîâà
|
| Abstract |
We consider Szego type inequality, where the norm of the derivatives of the conjugate
trigonometric polynomials is measured by the norm of the polynomial itself in $L_0$ space. We
improve the estimate of the constant in it, which was got by V. V. Arestov before. |
| Keywords |
derivatives of the polynomials; conjugate trigonometric polynomial; L_0 space; Szego inequality |
| Reference |
1. Mahler K. On the zeros of the derivative of a polynomial// Proc. Roy. Soc. London Ser. A. – 1961. –
V.264, ¹1317. - P. 145–154.
2. Zigmund A. Trigonometric series. V.1,2. Cambridge Univ. Press, 1959.
3. Taikov L.V. On conjugate trigonometric polynomials// Mat. Notes. – 1990. – V.48, ¹4. – P. 110–114. (in
Russian)
4. Arestov V.V. The Szeg.o inequality for derivatives of a conjugate trigonometric polynomial in $L_0$// Mat.
Notes. – 1994. – V.56, ¹6. – P. 10–26. (in Russian)
5. Adamov A.N. About conjugate trigonometric polynomials in $L_0$// Donetsk national university journal,
ser. A: nat. sciences. – 2011. – V.2. (in Russian)
6. Szeg.o G. Uber einen Satz des Hern Serge Bernstein// Schrift. K.onigsberg. Gelehrten Gesellschaft. – 1928.
– V.5, ¹4. – P. 59–70.
7. Ryzhik I. M, Gradstein I.S. Tables of integrals, sums, series and products. Moscow, Leningrad 1951. (in
Russian)
8. Dzyadyk V.K. Introduction to the theory uniform approximation of functions by polynomials. – M.:Nauka,
1977. – 512 p. (in Russian)
|
| Pages |
147-154 |
| Volume |
37 |
| Issue |
2 |
| Year |
2012 |
Journal |
Matematychni Studii |
| Full text of paper |
PDF |
| Table of content of issue |
HTML |