A one-parameter family of operators defined on analytic functions in a circle

1980 ◽  
pp. 292-300
Author(s):  
Yûsaku Komatu
Keyword(s):  
Analytic Functions ◽  
Parameter Family

scholarly journals PROPERTIES OF THE INVARIANT DISK PACKING IN A MODEL BANDPASS SIGMA–DELTA MODULATOR

2003 ◽  
Vol 13 (03) ◽  
pp. 631-641 ◽  
Author(s):  
PETER ASHWIN ◽  
XIN-CHU FU ◽  
JONATHAN DEANE
Keyword(s):  
Phase Space ◽  
Analytic Functions ◽  
Parameter Family ◽  
Sigma Delta Modulator ◽  
Sigma Delta ◽  
Disk Packing ◽  
Piecewise Isometries ◽  
Map Operations ◽  
Countably Infinite ◽  
Parameter Values

In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–Δ modulator. The periodically coded regions form a packing of the forward invariant phase space by invariant disks. For this one-parameter family of PWIs, by introducing codings underlying the map operations we give explicit expressions for the centers of the disks by analytic functions of the parameters, and then show that tangencies between disks in the packings are very rare; more precisely they occur on parameter values that are at most countably infinite. We indicate how similar results can be obtained for other plane maps that are piecewise isometries.

scholarly journals Cesáro type operators on spaces of analytic functions

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 85-97 ◽  
Author(s):  
S. Naik
Keyword(s):  
Hardy Space ◽  
Analytic Functions ◽  
Bloch Space ◽  
Bounded Operator ◽  
Parameter Family ◽  
Spaces Of Analytic Functions ◽  
Two Parameter

In this article, we consider a two parameter family of generalized Ces?ro operators P b,c , Re (b + 1) > Re c > 0, on classical spaces of analytic functions such as Hardy (H p ), BMOA and a- Bloch space (Ba). We Prove that P b,c, Re(b+1)>Re c > 0 is bounded on H p if and only if p ?(0, ?) and on Ba if and only if a ? (1, ?) and unbounded on H ?, BMOA and Ba, a ?(0, 1]. Also we prove that ?-Cesaro operators C? is a bounded operator from the Hardy space H p to the Bergmann space Ap for p ? (0, 1). Thus, we improve some well known results of the literature.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions
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