Trigonometric Orthogonal Systems

Cvetković, Aleksandar S.; Stanić, Marija P.

doi:10.1007/978-1-4419-6594-3_8

Cited by 7 publications

(9 citation statements)

References 16 publications

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“…The second interesting case is of a π-periodic weight function, i.e., w(x) = w(x + π), x ∈ [−π, 0). The following theorem was proved in [2]. Theorem 2.1.…”

Section: π-Periodic Weight Functionmentioning

confidence: 98%

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A trigonometric orthogonality with respect to a nonnegative Borel measure

Milovanović

Cvetković²,

Stanić

2012

Filomat

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In this paper we consider trigonometric polynomials of semi-integer degree orthogonal with respect to a linear functional, defined by a nonnegative Borel measure. By using a suitable vector form we consider the corresponding Fourier sums and reproducing kernels for trigonometric polynomials of semiinteger degree. Also, we consider the Christoffel function, and prove that it satisfies extremal property analogous with the algebraic case.

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“…The second interesting case is of a π-periodic weight function, i.e., w(x) = w(x + π), x ∈ [−π, 0). The following theorem was proved in [2]. Theorem 2.1.…”

Section: π-Periodic Weight Functionmentioning

confidence: 98%

“…The first results on orthogonal trigonometric polynomials of semi-integer degree on [0, 2π) with respect to a suitable weight function were given in 1959 by Abram Haimovich Turetzkii (see [8]). Such orthogonal systems were studied in detail in [2,4,5].…”

Section: Introductionmentioning

confidence: 99%

A trigonometric orthogonality with respect to a nonnegative Borel measure

Milovanović

Cvetković²,

Stanić

2012

Filomat

View full text Add to dashboard Cite

show abstract

“…where f 3 is given by (16). By changing (12) in the sum on the right hand side of (2) and using D 0, it is easy to see that…”

Section: Proofmentioning

confidence: 99%

“…In what follows, we consider quadrature rule with maximal trigonometric degree of exactness, that is, such that R n ( f ) = 0,

f MathClass-rel\in {scriptT}_{2 n MathClass-bin- 1 MathClass-bin+ 2 γ}

\overset{n}{false} MathClass-rel= 2 (n MathClass-bin- 1 MathClass-bin∕ 2 MathClass-bin+ γ)

, γ ∈ {0,1 ∕ 2}, in the case when weight function w is even on ( − π , π ). The corresponding orthogonal trigonometric polynomials (of integer or semi‐integer degree) are given by (see )