[63–1] On Bi-Orthogonal Systems of Trigonometric Polynomials

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

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Approximation of Ω—bandlimited Functions by Ω—bandlimited Trigonometric Polynomials

Sampling Theory, Signal Processing, and Data Analysis ◽

10.1007/bf03549477 ◽

2007 ◽

Vol 6 (3) ◽

pp. 273-296 ◽

Cited By ~ 2

Author(s):

R. Martin

Keyword(s):

Trigonometric Polynomials ◽

Bandlimited Functions

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An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

Mathematica Slovaca ◽

10.1515/ms-2017-0374 ◽

2020 ◽

Vol 70 (3) ◽

pp. 599-604

Author(s):

Şahsene Altinkaya

Keyword(s):

Error Function ◽

Trigonometric Polynomials ◽

Error Functions ◽

The Family ◽

Coefficient Inequalities

AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined by$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

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XVI.—On Triple Systems of Surfaces and Non-Orthogonal Curvilinear Coordinates

Proceedings of the Royal Society of Edinburgh ◽

10.1017/s0370164600021982 ◽

1927 ◽

Vol 46 ◽

pp. 194-205 ◽

Cited By ~ 3

Author(s):

C. E. Weatherburn

Keyword(s):

Curvilinear Coordinates ◽

Triple Systems ◽

Orthogonal Curvilinear Coordinates ◽

Orthogonal Systems ◽

Considerable Detail

The properties of “triply orthogonal” systems of surfaces have been examined by various writers and in considerable detail; but those of triple systems generally have not hitherto received the same attention. It is the purpose of this paper to discuss non-orthogonal systems, and to investigate formulæ in terms of the “oblique” curvilinear coordinates u, v, w which such a system determines.

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SOME ESTIMATES FOR POLYNOMIALS

Asian-European Journal of Mathematics ◽

10.1142/s1793557109000352 ◽

2009 ◽

Vol 02 (03) ◽

pp. 425-434

Author(s):

Tatsuhiro Honda ◽

Mitsuhiro Miyagi ◽

Masaru Nishihara ◽

Seiko Ohgai ◽

Mamoru Yoshida

Keyword(s):

Trigonometric Polynomials ◽

Alternative Proof ◽

Bernstein Inequalities

We give an elementary alternative proof of the Bernstein inequalities and the Szegö inequalities for trigonometric polynomials or polynomials.

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Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces

Georgian Mathematical Journal ◽

10.1515/gmj-2015-0059 ◽

2016 ◽

Vol 23 (1) ◽

Cited By ~ 2

Author(s):

Nina Danelia ◽

Vakhtang Kokilashvili

Keyword(s):

Lebesgue Space ◽

Variable Exponent ◽

Trigonometric Polynomials ◽

Lebesgue Spaces ◽

Variable Exponent Lebesgue Space ◽

Grand Lebesgue Spaces ◽

Direct And Inverse Theorems ◽

Inverse Theorems ◽

Grand Lebesgue Space

AbstractIn this paper we establish direct and inverse theorems on approximation by trigonometric polynomials for the functions of the closure of the variable exponent Lebesgue space in the variable exponent grand Lebesgue space.

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