Rewayat Khan
We introduce a generalized Crofoot transform between the model spaces corresponding to matrix-valued inner functions. As an application, we obtain results about matrix-valued truncated Toeplitz operators.
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Matrix valued asymmetric truncated Toeplitz operator are compression of multiplication operators acting between two model spaces. These are the generalization of matrix valued truncated Toeplitz operators. In this paper we use generalized Crofoot transform to characterize symbol of matrix valued asymmetric truncated Toeplitz operator equal to zero operator.
For a quasi-free module over a function algebra $A(Ω)$, we define an analogue of the Berezin transform and relate this to the quotient of the C*-algebra it generates modulo the commutator ideal.
In this paper, some more properties of the generalized principal pivot transform are derived. Necessary and sufficient conditions for the equality between Moore-Penrose inverse of a generalized principal pivot transform and its complementary generalized principal pivot transform are presented. It has been shown that the generalized principal pivot transform preserves the rank of symmetric part of a given square matrix. These results appear to be more generalized than the existing ones. Inheritance property of $P_{\dagger}$-matrix are also characterized for generalized principal pivot transform…
The purpose of this article is to present the second type fundamental relationship between the generalized Fourier--Feynman transform and the generalized convolution product on Wiener space. The relationships in this article are also natural extensions (to the case on an infinite dimensional Banach space) of the structure which exists between the Fourier transform and the convolution of functions on Euclidean spaces.
In this paper the generalized Radon transform over level hypersurfaces of CES-functions of measures supported in positive orthant is studied. A characterization of the generalized Radon transform of nonnegative measures is found. Explicit inversion formula for the generalized Radon transform of absolutely continuous measures is obtained.
In this paper wavelet functions are introduced in the context of $q$-theory. We precisely extend the case of Bessel and $q$-Bessel wavelets to the generalized $q$-Bessel wavelets. Starting from the $(q,v)$-extension ($v=(α,β)$) of the $q$-case, associated generalized $q$-wavelets and generalized $q$-wavelet transforms are then developed for the new context. Reconstruction and Plancherel type formulas are proved.
In the present article we consider the uniqueness problem for the generalized Radon transform arising in a mathematical model of production. We prove uniqueness theorems for this transform and for the profit function in the corresponding model of production. Our approach is based on the multidimensional Wiener's approximation theorems.
In this paper we obtain various results involving the generalized analytic Fourier-Feynman transform and the first variation of functionals in a Fresnel type class defined on the product function space $C_{a,b}^2[0,T]$.
Decay of Fourier transforms and generalized Besov spaces
本文通过傅里叶变换衰减特性特征化广义Lipschitz和贝索夫空间，并获得Titchmarsh型条件。
In the present paper, we prove for the Dunkl transform which generalizes the Fourier transform, weighted inequalities when the weights belong to the well known class Bp. As application, we obtain for power weights Pitt's inequality.
In this paper, certain generalized fractional derivative formulae are introduced involving the k-Mittag-Leffler function. Then their image formulae (using Beta transform, Laplace transform and Whittaker transform) are also established. The results obtained here are quite general in nature. The special cases of our findings are also discussed.
In this paper, we study the class of tempered distributions whose Fourier transform is a translation bounded measure and show that each such distribution in $\mathbb{R}^d$ has order at most $2d$. We show the existence of the generalized Eberlein decomposition within this class of distributions, and its compatibility with all previous Eberlein decompositions. The generalized Eberlein decomposition for Fourier transformable measures and properties of its components are discussed. Lastly, we take a closer look at the absolutely continuous spectrum of measures supported on Meyer sets.
Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. The main focus of this article is interrelation between generalized cosine transforms of different kinds in the context of their application to investigation of a certain family of intersection bodies, which we call $\lam$-intersection bodies. The latter include $k$-intersection bodies (in the sense of A. Koldobsky) and unit balls of finite-dimensional subspaces of $L_p$-spaces. In particul…
We first characterize the image of the compactly supported smooth even functions under the q-Weinstein transform as a subspace of the Schwartz space. We then describe the space of smooth $L_{α, q, a}^{2}$-functions whose q-Weinstein transform has compact support as a subspace of the space of $L_{α, q, a}^{2}$-functions.
In this paper we study generalized J-inner matrix valued functions which appear as resolvent matrices in various indefinite interpolation problems. Reproducing kernel indefinite inner product spaces associated with a generalized J-inner matrix valued function W are studied and intensively used in the description of the range of the linear fractional transformation associated with W and applied to the Schur class. For a subclass of generalized J-inner matrix valued function W the notion of associated pair is introduced and factorization formulas for W are found.
Abelian and Tauberian Results for the Fractional Hankel Transform of Generalized Functions
本文通过分数阶 Hankel 变换研究分布的拟渐近行为，提出了连接 Zemanian 空间中广义函数渐近性与其变换渐近性的 Tauber 型结果，并建立了分布分数阶 Hankel 变换的初值与终值定理。
Products of Berezin Transforms on Generalized Fock Spaces
该研究针对复空间ℂᵈ上广义Fock空间的Berezin变换乘积，对m≠2建立了参数唯一性结论，还刻画了Berezin变换的可交换性及乘积性质。
The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of intersections bodies in convex geometry.
In this paper, we prove the Hardy-Littlewood inequality for the generalized Fourier transform on Chébli-Triméche hypergroups and we study in the particular case of the Jacobi hypergroup the integrability of this transform on Besov-type spaces.
Let (M,g) be an analytic, compact, Riemannian manifold with boundary, of dimension n >= 2. We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker condition [23]. Using analytic microlocal analysis, we prove a microlocal regularity theorem for generalized Radon transforms on analytic manifolds defined on an analytic family of hypersurfaces. We then show injectivity and stability for an open, dense subset of smooth generalized Radon transforms satisfying the Bolker condition, including the analytic ones.
In this paper, the mean value formula depends on the Bessel generalized shift operator corresponding to the solutions of the boundary value problem related to the Bessel operator are studied. In addition to, Riesz Bessel transforms related to the Bessel operators are studied. Since Bessel generalized shift operator is translation operator corresponding to the Bessel operator, we construct a family of RBxj by using Bessel generalized shift operator. Finally, we analysis weighted inequalities involving Riesz Bessel transforms .
In this paper, we introduce a discrete Riesz transforms associated with the non-symmetric trigonometric Heckman-Opdam polynomials of type $A_1$. We prove that they can be extended to a bounded operators on $\ell^p(\mathbb{Z})$, $1<p<\infty$.
While dealing with a class of generalized Bergman spaces on the unit ball, we construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the Berezin transforms attached to these spaces. Finally, a new formula representing these transforms a functions of the Laplace-Beltrami operator is established in terms ofWilson polynomials by using the Fourier-Helgason transform.
We continue studies of Moutard-type transforms for the generalized analytic functions started in arXiv:1510.08764, arXiv:1512.00343. In particular, we show that generalized analytic functions with the simplest contour poles can be Moutard transformed to the regular ones, at least, locally. In addition, the later Moutard-type transforms are locally invertible.
We continue the studies of Moutard-type transform for generalized analytic functions started in our previous paper: arXiv:1510.08764. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that in the framework of this approach Moutard-type transforms for the aforementioned functions commute with holomorphic changes of variables.
We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.
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