Expansion of analytic functions in exponential polynomials

AbstractIn this paper we characterize all subspaces of analytic functions in finitely generated shift-invariant spaces with compactly supported generators and provide explicit descriptions of their elements. We illustrate the differences between our characterizations and Strang-Fix or zero conditions on several examples. Consequently, we depict the analytic functions generated by scalar or vector subdivision with masks of bounded and unbounded support. In particular, we prove that exponential polynomials are indeed the only analytic limits of level dependent scalar subdivision schemes with finitely supported masks.

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Distributional boundary values of analytic functions and positive definite distributions

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2015.2.4 ◽

2015 ◽

Vol 20 (2) ◽

pp. 210-225

Author(s):

Saulius Norvidas ◽

Keyword(s):

Analytic Functions ◽

Positive Definite ◽

Boundary Values

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Coefficient Bounds for Certain Subclass of Analytic Functions Defined By Quasi-Subordination

Iraqi Journal of Science ◽

10.24996/ijs.2018.59.2c.16 ◽

2018 ◽

Vol 59 (2C) ◽

Keyword(s):

Analytic Functions ◽

Coefficient Bounds

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The radii of starlikeness of order alpha of certain classes of analytic functions associated with the classes T of totally monotonie functions, N2 of Nevanlinna analytic functions and ON2 of odd Nevanlinna analytic functions

Bulletin de la Classe des sciences ◽

10.3406/barb.1994.27575 ◽

1994 ◽

Vol 5 (7) ◽

pp. 401-408

Author(s):

Pavel G. Todorov

Keyword(s):

Analytic Functions

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

Ukrainian Mathematical Bulletin ◽

10.37069/1810-3200-2020-17-2-7 ◽

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.

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