Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$, where $alpha>-frac{1}{2}$ and $1

Abstract. Block sequences with respect to frames in Hilbert spaces have been defined. Examples have been provided to show that a block sequence with respect to a given frame may not even be a Bessel sequence. Also, a necessary and sufficient condition under which a block sequence with respect to a frame is a frame has been given. Further, applications of block sequences to obtain Fusion frames ...

We show that the use of operational methods and of multi-index Bessel functions allow the derivation of generating functions, involving the product of an arbitrary number of Laguerre polynomials. ∗2000 Mathematics Subject Classification. 33C45, 44A45. †E-mail:[email protected] ‡E-mail:[email protected] §E-mail:[email protected] ¶E-mail:[email protected] 270 G. Dattol...

We propose a method to dynamically control the Fano resonance of a ring/crescent-ring gold nanostructure by spatially changing the phase distribution of a probe Bessel beam. We demonstrate that a highly tunable Fano interference between the quadrupole and bright dipole modes can be realized in the near-infrared range. Even though a complex interference between a broad resonance and a narrower r...

Image quality in light-sheet fluorescence microscopy is strongly affected by the shape of the illuminating laser beam inside embryos, plants or tissue. While the phase of Gaussian or Bessel beams propagating through thousands of cells can be partly controlled holographically, the propagation of fluorescence light to the detector is difficult to control. With each scatter process a fluorescence ...

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...