Teoplitz matrices of fourier coefficients of piecewise-continuous functions

1968 ◽  
Vol 1 (2) ◽  
pp. 166-167
Author(s):  
I. Ts. Gokhberg
Keyword(s):  
Fourier Coefficients ◽  
Continuous Functions ◽  
Piecewise Continuous

Approximation of Piecewise Continuous Functions by Quotients of Bounded Analytic Functions

1972 ◽  
Vol 24 (4) ◽  
pp. 642-657 ◽  
Author(s):  
Donald Sarason
Keyword(s):  
Banach Algebra ◽  
Analytic Functions ◽  
Fourier Coefficients ◽  
Continuous Functions ◽  
Affirmative Answer ◽  
Bounded Analytic Functions ◽  
Closed Subalgebra ◽  
Boundary Functions ◽  
Piecewise Continuous ◽  
Complex Valued

This paper concerns a certain subalgebra of the Banach algebra of complex valued, essentially bounded, Lebesgue measurable functions on the unit circle in the complex plane (denoted here by L∞). My interest in this subalgebra was prompted by a question of R. G. Douglas. Let H∞ denote the space of functions in L∞ whose Fourier coefficients with negative indices vanish (equivalently, the space of boundary functions for bounded analytic functions in the unit disk). Douglas [5] has asked whether every closed subalgebra of L∞ containing H∞ is determined by the functions in H∞ that it makes invertible. More precisely, is such an algebra generated by H∞ and the inverses of the functions in H∞ that are invertible in the algebra? An affirmative answer is known for L∞ itself and for certain subalgebras of L∞ recently studied by Davie, Gamelin, and Garnett [3]. At the time of this writing, no algebra is known for which the above question can be answered negatively.

scholarly journals Restriction of Families of Conversion Operators in Lp Spaces

2021 ◽  
Vol 27 (3) ◽  
pp. 449-460
Author(s):  
A. D. Nakhman
Keyword(s):  
Fourier Coefficients ◽  
Continuous Functions ◽  
Parameter Family ◽  
Maximal Operators ◽  
Limiting Behavior ◽  
Lp Spaces ◽  
Almost Everywhere ◽  
Spaces Of Continuous Functions

We study a one-parameter family of convolutional operators acting in Lebesgue Lp spaces. The case of integral kernels given by the Fourier coefficients is considered. It is established that the condition of the coefficients being quasiconvex ensures the boundedness of the corresponding maximal operators. The limiting behavior of families in the metrics of spaces of continuous functions and Lp, p ≥ 1, classes is studied, and their convergence is obtained almost everywhere. The ways of possible generalizations and distributions are indicated.

Note on an Application of the δ-Function in the Representation of Solutions of Algebraic Equations

1967 ◽  
Vol 10 (5) ◽  
pp. 735-738
Author(s):  
J. B. Sabat
Keyword(s):  
Continuous Function ◽  
Delta Function ◽  
Continuous Functions ◽  
Dirac Delta Function ◽  
Algebraic Equations ◽  
Dirac Delta ◽  
Representation Of Solutions ◽  
Piecewise Continuous ◽  
Image Position

The “function” δ(x - xo) is known as the Dirac Delta function and may be defined as zero everywhere except at xo, where it is infinite in such a way that1having property that for every continuous function φ(x) on (a, b)2It is well known [2] δ(x-xo) can be approximated as a limit of a sequence of piecewise continuous functions, and there is an abundance of such sequences.

Some explicit results on one kind of sticky diffusion

2019 ◽  
Vol 56 (2) ◽  
pp. 398-415
Author(s):  
Yiming Jiang ◽  
Shiyu Song ◽  
Yongjin Wang
Keyword(s):  
Diffusion Process ◽  
Continuous Functions ◽  
Price Dynamics ◽  
Call Option ◽  
Distributional Properties ◽  
Financial Application ◽  
Piecewise Continuous

AbstractIn this paper we derive several explicit results on one special sticky diffusion process which is constructed as a time-changed version of a diffusion with no sticky points. A theorem concerning the process-related Green operators defined on some nonnegative piecewise continuous functions is provided. Then, based on this theorem, we explore the distributional properties of the sticky diffusion. A financial application is presented where we compute the value of the European vanilla call option written on the underlying with sticky price dynamics.

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