FUNCTIONS WITH SPLINE SPECTRA AND THEIR APPLICATIONS

2010 ◽  
Vol 08 (02) ◽  
pp. 197-223 ◽  
Author(s):  
QIUHUI CHEN ◽  
CHARLES A. MICCHELLI ◽  
YI WANG
Keyword(s):  
Real Axis ◽  
Real Line ◽  
Analytic Functions ◽  
Signal Analysis ◽  
Sinc Function ◽  
The Real ◽  
Sampling Formula

In this paper, we introduce a family of real-valued functions which have spline spectra. They extend the well-known Sinc function and generally are the restrictions to the real line of analytic functions in a strip containing the real axis. We investigate various properties of these functions including those related to interpolation, orthogonality, and stability. Moreover, a sampling formula is provided for their construction and some applications for signal analysis are given.

On the approximation of analytic functions in a strip

1985 ◽  
Vol 97 (3) ◽  
pp. 381-384 ◽  
Author(s):  
Dieter Klusch
Keyword(s):  
Entire Function ◽  
Real Axis ◽  
Exponential Type ◽  
Uniform Approximation ◽  
Analytic Functions ◽  
Trigonometric Polynomials ◽  
The Real ◽  
Image Position ◽  
Class Of Functions

1. Letand denote by Aδ the class of functions f analytic in the strip Sδ = {z = x + iy| |y| < δ}, real on the real axis, and satisfying |Ref(z)| ≤ 1,z∊Sδ. Then N.I. Achieser ([1], pp. 214–219; [8], pp. 137–8, 149) proved that each f∊Aδ can be uniformly approximated on the whole real axis by an entire function fc of exponential type at most c with an errorwhere ∥·∥∞ is the sup norm on ℝ. Furthermore ([7], pp. 196–201), if f∊Aδ is 2π-periodic, then the uniform approximation Ẽn (Aδ) of the class Aδ by trigonometric polynomials of degree at most n is given by

Extremal Problems for the Classes SR-p and TR-p

1990 ◽  
Vol 42 (4) ◽  
pp. 619-645
Author(s):  
Walter Hengartner ◽  
Wojciech Szapiel
Keyword(s):  
Uniform Convergence ◽  
Linear Space ◽  
Unit Disk ◽  
Real Axis ◽  
Analytic Functions ◽  
Dual Space ◽  
Extremal Problems ◽  
Space Of Analytic Functions ◽  
The Real

Let H(D) be the linear space of analytic functions on a domain D of ℂ endowed with the topology of locally uniform convergence and let H‘(D) be the topological dual space of H(D). For domains D which are symmetric with respect to the real axis we use the notation Furthermore, denote by S the set of all univalent mappings f defined on the unit disk Δ which are normalized by f (0) = 0 and f‘(0) =1.

Starlike Univalent Functions Bounded on the Real Axis

1989 ◽  
Vol 41 (4) ◽  
pp. 642-658
Author(s):  
Richard Fournier
Keyword(s):  
Real Axis ◽  
Analytic Functions ◽  
Unit Disc ◽  
Univalent Functions ◽  
Uniform Norm ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Real ◽  
Typically Real ◽  
Image Position

We denote by E the open unit disc in C and by H(E) the class of all analytic functions f on E with f(0) = 0. Let (see [3] for more complete definitions)S = {ƒ ∈ H(E)|ƒ is univalent on E}S0 = {ƒ ∈ H(E)|ƒ is starlike univalent on E}TR = {ƒ ∈ H(E)|ƒ is typically real on E}.The uniform norm on (— 1, 1) of a function ƒ ∈ H(E) is defined by

scholarly journals Class of Analytic Functions Defined by q-Integral Operator in a Symmetric Region

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1042 ◽  
Author(s):  
Lei Shi ◽  
Mohsan Raza ◽  
Kashif Javed ◽  
Saqib Hussain ◽  
Muhammad Arif
Keyword(s):  
Integral Operator ◽  
Real Axis ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
The Real ◽  
New Class ◽  
Symmetric Region ◽  
Inverse Coefficient

The aim of the present paper is to introduce a new class of analytic functions by using a q-integral operator in the conic region. It is worth mentioning that these regions are symmetric along the real axis. We find the coefficient estimates, the Fekete–Szegö inequality, the sufficiency criteria, the distortion result, and the Hankel determinant problem for functions in this class. Furthermore, we study the inverse coefficient estimates for functions in this class.

scholarly journals FEKETE-SZEGO problem for a class of analytic functinos defined by convolution

2013 ◽  
Vol 44 (2) ◽  
pp. 187-195 ◽  
Author(s):  
Sivaprasad Kumar Shanmugam ◽  
Virendra Kumar
Keyword(s):  
Real Axis ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Real Numbers ◽  
The Real ◽  
Alpha Beta

Let $g$ and $h$ be two fixed normalized analytic functions and $\phi$ be starlike with respect to $1,$ whose range is symmetric with respect to the real axis. Let $\mathcal{M}^{\alpha,\beta}_{g,h}(\phi)$ be the class of analytic functions $f(z)=z+a_2z^2+a_3z^3+\ldots$, satisfying the subordination $$\left(\frac{(f*g)(z)}{z}\right)^\alpha \left(\frac{(f*h)(z)}{z}\right)^{\beta}\prec \phi(z),$$ where $\alpha$ and $\beta$ are real numbers and are not zero simultaneously. In the present investigation, sharp upper bounds of the Fekete-Szego functional $|a_3-\mu a_2^2|$ for functions belonging to the class $\mathcal{M}^{\alpha,\beta}_{g,h}(\phi)$ are obtained and certain applications are also discussed.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

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