Showing papers in "Integral Transforms and Special Functions in 2019"
TL;DR: In this paper, the Wright hypergeometric matrix functions and incomplete Wright Gauss matrix functions by using Pochhammer matrix symbol have been studied and the Wright matrix functions have been introduced.
Abstract: In this paper we focus on the Wright hypergeometric matrix functions and incomplete Wright Gauss hypergeometric matrix functions by using Pochhammer matrix symbol. We first introduce the Wright hyp...
34 citations
TL;DR: In this paper, the necessary and sufficient conditions for the boundedness of commutators of fractional integral operators on mixed Morrey spaces were given, and the predual spaces of mixed M... were constructed.
Abstract: In this paper, we give the necessary and sufficient conditions for the boundedness of commutators of fractional integral operators on mixed Morrey spaces. We construct the predual spaces of mixed M...
29 citations
TL;DR: In this paper, the Fourier-Jacobi harmonic analysis was used to study the problem of approximating functions in weighted L 2 function spaces on the half-axis [0, + ∞).
Abstract: We use the methods of Fourier–Jacobi harmonic analysis to study problems of the approximation of functions in weighted L2 function spaces on the half-axis [0,+∞). We prove analogues of Jack...
19 citations
TL;DR: In this article, the authors define radial multipliers using solutions of the Helmholtz equation, which depend on the radial coordinate, and find the recurrence relations between them in the space of any dimension m>1.
Abstract: We define radial multipliers using solutions of the Helmholtz equation, which depend on the radial coordinate, and we find the recurrence relations between them in the space of any dimension m>1, i...
17 citations
TL;DR: In this article, the set of general polynomial sequences is considered and an elementary systematic approach is proposed, in which a structure of group is given and for every element of this group recurre...
Abstract: In this paper the set of general polynomial sequences is considered. An elementary systematic approach is proposed. In fact a structure of group is given and for every element of this group recurre...
15 citations
TL;DR: In this paper, the quaternion windowed Fourier transform (QWFT) was studied and the Local uncertainty principle, the Logarithmic uncertainty principle and Amrein Berthier's radar was proved.
Abstract: In this paper, we study the quaternion windowed Fourier transform (QWFT) and prove the Local uncertainty principle, the Logarithmic uncertainty principle and Amrein Berthier for the QWFT, the radar...
14 citations
TL;DR: In this paper, the sum of the sums given by S1(l,n) and S3(n) for integers l≥ 2 and n≥ 1, respectively, is shown to be √ k = 0n(− 1)k(2lk+1)k!31lk3.
Abstract: For integers l≥ 2 and n≥ 1, denote by S1(l,n) and S3(l,n) the sums given by S1(l,n):=∑k=0n(−1)k(2lk+1)k!31lk3 and S3(l,n):=∑k=0n(−1)k(2lk+1)3k!31lk3, respectively. In this paper, we deduce ...
13 citations
TL;DR: In this paper, special generating functions and Mehler's formula for the univariate complex Hermite polynomials are obtained and next employed to introduce and study some one-and two-dimensional integral transfo...
Abstract: Special generating functions and Mehler's formula for the univariate complex Hermite polynomials are obtained and next employed to introduce and study some one- and two-dimensional integral transfo...
12 citations
TL;DR: In this paper, the Riesz-type fractional differential equation is studied and its analytical solution is obtained for the equation defined on R, its existence and uniqueness of the solution are prove.
Abstract: In this paper, the Riesz-type fractional differential equation is studied. For the equation defined on R, its analytical solution is obtained. The existence and uniqueness of the solution are prove...
12 citations
TL;DR: In this paper, the Stein-Weiss inequality on general homogeneous Lie groups has been shown to hold for homogeneous lie groups with special properties of homogeneous norms, and the obtained results extend previously known inequalities.
Abstract: In this note, we prove the Stein–Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key ro...
12 citations
TL;DR: In this article, approximation properties of the Mellin-type nonlinear integral operators defined on multivariate functions are investigated, in order to get more general results than the classical a...
Abstract: In this study, approximation properties of the Mellin-type nonlinear integral operators defined on multivariate functions are investigated. In order to get more general results than the classical a...
TL;DR: In this paper, the zeta function Zpα(s;x) is defined for real numbers and complex numbers, with ℜ(s)>1−r, p≥1, and x+1>0.
Abstract: Let p,x be real numbers, and s be a complex number, with ℜ(s)>1−r, p≥1, and x+1>0. The zeta function Zpα(s;x) is defined by Zpα(s;x)=1Γ(s)∫0∞e−xtet−1Liα1−e−tpts−1dt, where α=(α1,…,αr) is a r-tuple ...
TL;DR: In this paper, the orthonormal polynomials with respect to the Sobolev-type inner product have been studied, and the inner product has been shown to be robust to noise.
Abstract: Let {qn(α,β,m)(x)}n≥0 be the orthonormal polynomials with respect to the Sobolev-type inner product ⟨f,g⟩α,β,m=∑k=0m∫−11f(k)(x)g(k)(x)dwα+k,β+k(x),α,β>−1,m≥1, where dwa,b(x)=(1−x)a(1+x)bdx. We obta...
TL;DR: In this paper, the authors investigated and reported new Euler identities of weight m+p+q+1, for m,p,q positive integers and m + p+q + 1.
Abstract: In this paper we develop new identities for Euler sums with rational argument. We shall investigate and report on new Euler identities of weight m+p+q+1, for m,p,q positive integers and m + p + q a...
TL;DR: The abstract Cauchy problem for the fractional evolution equation with the Caputo derivative of order β ∈(0,1) and operator −Aα, α∈( 0,1), where −A generates a strongly continu...
Abstract: The abstract Cauchy problem for the fractional evolution equation with the Caputo derivative of order β∈(0,1) and operator −Aα, α∈(0,1), is considered, where −A generates a strongly continu...
TL;DR: In this paper, using the Mellin transform of Wright function, an addition formula for the Wright function was derived using a special case of the Hermite, Bessel and Mittag-Leffl...
Abstract: In this paper, using the Mellin transform of Wright function we derive an addition formula for the Wright function. In some special cases, addition formulas for the Hermite, Bessel and Mittag-Leffl...
TL;DR: In this paper, the Hausdorff operator is bounded on the real Hardy space H1(R) and commuting relations for Hausorff operators and their corresponding commuting relations are discussed.
Abstract: Liflyand and Moricz in Liflyand and Moricz [The Hausdorff operator is bounded on the real Hardy space H1(R). Proc Amer Math Soc. 1999;128:1391–1396; Commuting relations for Hausdorff operators and ...
TL;DR: In this article, the wavelet packet approximation theorem for Hr type norm has been proved for weak derivatives of the type norm with equal distribution of the vanishing m. The authors showed that with the same distribution of vanishing m, they can measure the difference of the derivatives.
Abstract: In this paper, we give the wavelet packet approximation theorem for Hr type norm which can measure difference of the (weak) derivatives. We will show that with equal distribution of the vanishing m...
TL;DR: In this article, the generalized Jacobi translation constructed by the Jacobi operator was studied and the generalized modulus of smoothness in the space L 2 (L 2 ) was defined.
Abstract: In this paper, we study the generalized Jacobi translation constructed by the Jacobi operator. Using the generalized Jacobi translation, we define generalized modulus of smoothness in the space L2(...
TL;DR: In this article, the authors obtained the new results of the strong and weak Spanne-Guliyev and Adams-Gunawan type boundedness characterization of the maximal operator Mα in generality.
Abstract: In this paper, we will obtain the new results of the strong and weak Spanne-Guliyev, Adams-Guliyev and Adams-Gunawan type boundedness characterization of the fractional maximal operator Mα in gener...
TL;DR: A sampling theorem associated with ST is proposed which is based on multiresolution subspace and truncation and aliasing error generated due to the sampling process are derived.
Abstract: S-transform (ST) is an extension of wavelet transform (WT) and short-time Fourier transform (STFT). The ST is depended on a scalable and moving Gaussian window. It overcomes the low-resolution factor of STFT and tackles with a lack of phase in WT. The ST is a useful tool for signal processing and analysis. In this paper, the multiresolution analysis (MRA) related with ST is introduced and after that a sampling theorem associated with ST is proposed which is based on multiresolution subspace. Additionally, truncation and aliasing error generated due to the sampling process, are also derived. The theoretical determinations are exhibited and validated using simulation results.
TL;DR: In the literature on spectral differential equations with polynomial eigenfunctions, Koornwinder's generalized Laguerre polynomials are playing a prominent role.
Abstract: In the enduring, fruitful research on spectral differential equations with polynomial eigenfunctions, Koornwinder's generalized Laguerre polynomials are playing a prominent role. Being orthogonal o...
TL;DR: The other properties of a finite field analogue for the Appell series are studied, which can be considered as finite field analogues for the classical one.
Abstract: He et al. [Finite Fields and Their Applications 48 (2017), 289–305] introduced a finite field analogue for the Appell series F2 and derived its transformations, reduction formulas as well a...
TL;DR: In this article, a finite set of positive integers G and polynomials Rg, g∈G, with degree Rg equal to g, were associated to a sequence (qn(x))n of Charlier type polynomial defined from the Charlier poly.
Abstract: Given a finite set of positive integers G and polynomials Rg, g∈G, with degree of Rg equal to g, we associate to them a sequence (qn(x))n of Charlier type polynomials defined from the Charlier poly...
TL;DR: In this paper, a new proof of Wimp's formula for the associated Pollaczek polynomials Pnλz;a,b,c,d,e,f,c was presented.
Abstract: This paper is mainly devoted to generating functions of Pollaczek and other related polynomials. We first present a new proof of Wimp's formula for the associated Pollaczek polynomials Pnλz;a,b,c. ...
TL;DR: In this article, a simple ℵ-function and its dynamic equation is presented, and an application to give an analytical solution to the Black Scholes equation was presented, based on a simple π-function.
Abstract: A simple ℵ-function and its dynamic equation is presented. An application to give an analytical solution to the Black Scholes equation is presented.
TL;DR: The construction of strictly positive definite models has become one of the most important problems in multivariate approximation and spatial statistics as mentioned in this paper, and it has been shown to be NP-hard.
Abstract: Positive definite matrix functions on spheres arise naturally in multivariate approximation and spatial statistics. The construction of strictly positive definite models has become one of the most ...
TL;DR: In this article, the authors introduce certain unified polynomials which can be specialized to yield a number of known polynomial and number classes, such as Fibonacci polynomorphisms and numbers.
Abstract: We aim to introduce certain unified polynomials which can be specialized to yield a number of known polynomials and numbers, for example, Pell polynomials and numbers, Fibonacci polynomials...
TL;DR: In this article, the Coulomb self-energy of a uniformly charged three-dimensional (3D) manifold was studied. But the authors focused on hypergeometric-type mathematical techniques.
Abstract: The article aims at studying hypergeometric-type mathematical techniques based on the extension of a model previously used to describe the Coulomb self-energy of a uniformly charged a three-dimensi...
TL;DR: In this article, the Jacobi numbers were introduced, which generalizes in a natural way several sequences that are known in the literature, such as the Riemann Jacobi sequence.
Abstract: In this paper we will introduce a sequence of complex numbers that are called the Jacobi numbers. This sequence generalizes in a natural way several sequences that are known in the literature, such...