Convolution Properties Research Articles

ON HADAMARD PRODUCT AND A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY SUBORDINATION

In this paper, making use of the convolution structure and subordination, we introduce a new subclass of analytic functions, estimate coefficient bounds and obtain integral representations of functions associated with this subclass. Some interesting consequences of convolution property of the class are also obtained.

Some properties of certain family of multiplier transforms

The main purpose of this paper is to derive some inequality properties, convolution properties, subordination and superordination properties, and sandwich-type results of a certain family of multiplier transforms.

Convolution and subordination properties of analytic functions with bounded radius rotations

Convolution and subordination properties of analytic functions with bounded radius rotations

Интегральные свойства обобщённых потенциаловтипа Бесселя и типа Рисса

In the paper we study integral properties of convolutions of functions with kernels generalizingthe classical Bessel-Macdonald kernels (), ∈ , 0 < < . The local behavior of Bessel-Macdonald kernels in the neighborhood of the origin are characterized by the singularity ofpower type ||-. The kernels of generalized Bessel-Riesz potentials may have non-powersingularities in the neighborhood of the origin. Their behavior at the infinity is restricted onlyby the integrability condition, so that the kernels with compact support are included too. In thepaper the general criteria for the embedding of potentials into rearrangement invariant spacesare concretized in the case when the basic space coincides with the weighted Lorentz space.We obtain the explicit descriptions for the optimal rearrangement invariant space for such anembedding.

Convolution properties for certain meromorphically multivalent functions

Let ?p denote the class of functions of the form f(z)=z-p + ??,n=p anzn (p ? N). Two new subclasses Hp,k(?,A,B) and Qp,k(?,A,B) of meromorphically multivalent functions starlike with respect to k-symmetric points in ?p are investigated. Certain convolution properties for these subclasses are obtained.

Some Convolution Properties of Multivalent Analytic Functions

In this paper, we introduce a new subclass of multivalent functions associated with conic domain in an open unit disk. We study some convolution properties, su cient condition for the functions belonging to this new class.

Depth resolution enhanced spatial filtering in integral imaging based on convolution property between periodic functions with interpolation method

We propose a depth resolution improved target depth image extraction method in integral imaging by using the convolution property between periodic functions (CPPF) with image interpolation algorithm. We derive the depth resolution equation of a direct pickup system and analyze the factors related to the change of the depth resolution which are the focal length of an elemental lens and the resolution of an elemental image. We investigate the effect according to the change of these factors. The simulation results show that the key factor to change the depth resolution is the resolution of an elemental image. To show the feasibility of the proposed method, we carry out the preliminary experiments and present the results.

Applications of conic type regions to subclasses of meromorphic univalent functions with respect to symmetric points

In this paper, we define new subclasses of meromorphic univalent functions with respect to symmetric points. The convolution properties and coefficient bounds for these classes are studied.

Convolution Properties for Some Subclasses of Meromorphic Bounded Functions of Complex Order

Convolution Properties for Some Subclasses of Meromorphic Bounded Functions of Complex Order

Spectral Types of Linear $q$-Difference Equations and $q$-Analog of Middle Convolution

We give a $q$-analog of middle convolution for linear $q$-difference equations with rational coefficients. In the differential case, middle convolution is defined by Katz, and he examined properties of middle convolution in detail. In this paper, we define a $q$-analog of middle convolution. Moreover, we show that it also can be expressed as a $q$-analog of Euler transformation. The $q$-middle convolution transforms Fuchsian type equation to Fuchsian type equation and preserves rigidity index of $q$-difference equations.

Subclasses of meromorphicallyp-valent functions involving a certain linear operator

AbstractThe object of this paper is to investigate a series of inclusion relationships of two new subclassses of meromorphicallyp-valent functions, defined by means of a linear operator. We also study some integral preserving properties and convolution properties of the considered classes.

Singularity and Fine Fractal Properties of One Class of Infinite Bernoulli Convolutions with Essential Overlapping. II

We study the Lebesgue structure and fine fractal properties of infinite Bernoulli convolutions, i.e., the distributions of random variables of the form ξ = ∑ = 1 ∞ ξ k a k , where ∑ = 1 ∞ a k is a convergent positive series and ξ k are independent (generally speaking, nonidentically distributed) Bernoulli random variables. Our main aim is to investigate the class of Bernoulli convolutions with essential overlaps generated by a series ∑ = 1 ∞ a k such that, for any k ∈ ℕ, there exists s k ∈ ℕ ⋃{0} for which a k = a k+1 =…= $$ {a}_{k+{s}_k} $$ ≥ $$ {r}_{k+{s}_k} $$ and, in addition, s k > 0 for infinitely many indices k. In this case, almost all (both in a sense of Lebesgue measure and in a sense of fractal dimension) points of the spectrum have continuum many representations of the form ξ = ∑ = 1 ∞ e k a k with e k ∈ {0, 1}. It is shown that the probability measure μ ξ has either a pure discrete distribution or a pure singularly continuous distribution. We also establish sufficient conditions for the confidentiality of the family of cylindrical intervals on the spectrum $$ {S}_{\mu_{\xi }} $$ generated by the distributions of the random variable ξ. In the case of singularity, we also deduce the explicit formula for the Hausdorff dimension of the corresponding probability measure [i.e., the Hausdorff–Besicovitch dimension of the minimal supports of the measure μ ξ (in a sense of dimension)].

On a class of functions associated with Sălăgean operator

In this paper we define a new class of analytic functions using the Sălăgean operator and subordination. The geometric significance, radius problem, coefficient estimates and convolution properties have been discussed for functions belonging to this class.

Subclasses of Meromorphically Multivalent Functions Defined By a Differential Operator

In this paper we introduce and study two new subclasses \Sigma_{\lambda\mu mp}(\alpha,\beta)$ and $\Sigma^{+}_{\lambda\mu mp}(\alpha,\beta)$ of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of $% (n,\delta)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.

Integral Representations and Coefficient Estimates for a Subclass of Meromorphic Starlike Functions

In this paper, we introduce a natural subclass of meromorphic starlike functions in the open unit disk. Results concerning subordination properties, integral representations, properties of convolutions, inclusion relationship and coefficient inequalities for the functions of this class are derived. Furthermore, we solve radius problems for certain related classes of meromorphic strongly starlike functions and meromorphic parabolic starlike functions.

Some subclasses of meromorphic functions involving in the Hurwitz-Lerch Zeta function

The main purpose of this paper is to investigate some subclasses of meromorphic functions involving the meromorphic modified version of the familiar Srivastava-Attiya operator. Such results as inclusion relationships, convolution properties, coefficient inequalities, integralpreserving properties, subordination and superordination properties are proved.

Weak Lévy--Khintchine Representation for Weak Infinite Divisibility

A random vector ${\bf X}$ is weakly stable if and only if for all $a,b \in {\mathbb R}$ there exists a random variable $\Theta$ such that $a{\bf X} + b {\bf X}' \stackrel{d}{=} {\bf X} \Theta$, where ${\bf X}'$ is an independent copy of ${\bf X}$ and $\Theta$ is independent of ${\bf X}$. This is equivalent (see [J. K. Misiewicz, K. Oleszkiewicz, and K. Urbanik, Studia Math., 167 (2005), pp. 195--213]) to the condition that for all random variables $Q_1, Q_2$ there exists a random variable $\Theta$ such that ${\bf X} Q_1 + {\bf X}' Q_2 \stackrel{d}{=} {\bf X} \Theta,$ where ${\bf X}, {\bf X}', Q_1, Q_2, \Theta$ are independent. In this paper we define a weak generalized convolution of measures defined by the formula ${\cal L}(Q_1) \otimes_{\mu} {\cal L}(Q_2) = {\cal L}(\Theta),$ if the former equation holds for ${\bf X}, Q_1, Q_2, \Theta$ and $\mu = {\cal L}(\bf X)$. We study here basic properties of this convolution and basic properties of distributions which are infinitely divisible in the sense of this ...

Application of the Bernstein polynomials for solving Volterra integral equations with convolution kernels

In this article, we consider the second-type linear Volterra integral equations whose kernels based upon the difference of the arguments. The aim is to convert the integral equation to an algebraic one. This is achieved by approximating functions appearing in the integral equation with the Bernstein polynomials. Since the kernel is of convolution type, the integral is represented as a convolution product. Taylor expansion of kernel along with the properties of convolution are used to represent the integral in terms of the Bernstein polynomials so that a set of algebraic equations is obtained. This set of algebraic equations is solved and approximate solution is obtained. We also provide a simple algorithm which depends both on the degree of the Bernstein polynomials and that of monomials. Illustrative examples are provided to show the validity and applicability of the method.

CONVOLUTION PROPERTIES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS

The authors introduce two new subclasses of analytic functions. The object of the present paper is to investigate some convolution properties of functions in these subclasses.

FBMC System: An Insight into Doubly Dispersive Channel Impact

It has been claimed that filter bank multicarrier (FBMC) systems suffer from negligible performance loss caused by moderate dispersive channels in the absence of guard time protection between symbols. However, a theoretical and systematic explanation/analysis for the statement is missing in the literature to date. In this paper, based on one-tap minimum mean square error (MMSE) and zero-forcing (ZF) channel equalizations, the impact of doubly dispersive channel on the performance of FBMC systems is analyzed in terms of mean square error of received symbols. Based on this analytical framework, we prove that the circular convolution property between symbols and the corresponding channel coefficients in the frequency domain holds loosely with a set of inaccuracies. To facilitate analysis, we first model the FBMC system in a vector/matrix form and derive the estimated symbols as a sum of desired signal, noise, intersymbol interference (ISI), intercarrier interference (ICI), interblock interference (IBI), and estimation bias in the MMSE equalizer. Those terms are derived one-by-one and expressed as a function of channel parameters. The numerical results reveal that under harsh channel conditions, e.g., with large Doppler spread or channel delay spread, the FBMC system performance may be severely deteriorated and error floor will occur.