Some extremal problems for trigonometric polynomials

✍ Scribed by Eduard Belinsky

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 164 KB
• Volume: 286
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1016/s0022-247x(03)00509-2

✦ Synopsis

Three extremal problems for trigonometric polynomials are studied in this paper. The first was initiated by Maiorov. It relates to the trigonometric polynomials with n nonzero harmonics. The L p -norm of the Weyl derivative is compared with the L q -norm of the polynomial. The other two problems have appeared in the recent paper by Oswald. They deal with the polynomials of degree n. The minimum of L p -norm with respect to the choice of phases is compared with l q -norm of its coefficients.