Motivated by recent advances in canonical harmonic analysis for Sturm-Liouville transforms due to Soltani and collaborators, including Parseval-Goldstein type identities and Boas-type results for canonical Sturm-Liouville settings, we develop an Integral Transforms Composition Method (ITCM) for the canonical Bessel operator Delta nu m associated with the Ghazouani-Sahbani transform. By linking the classical Fourier-Bessel transform F nu to its canonical analogue F nu m via spectral unitary dilation, we establish a sharp spectral alignment identity. We construct unitary transmutation operators Sm and Pm that intertwine Delta nu m with the classical Bessel operator B nu . Using Weber-Sonine formulae, we derive closed-form kernels involving Bessel functions and quadratic phase factors. We apply this framework to the transport of wavelet admissibility from classical to canonical settings. These results extend the ITCM framework to Bessel operators with quadratic phase deformations, bridging classical and canonical harmonic analysis.
Periodically vector-valued Gabor analysis on the half real line R+=[0,infinity) has extensive applications in multiplexing-based fields. This paper addresses a class of vector-valued Gabor frames on discrete periodic subset of half the real line R+=[0,infinity) . Using 'circle plus'-based Zak transform, we characterize complete condition of Gabor systems, Gabor frames (Riesz bases, orthonormal bases) and (weak) Gabor duals on l2(S,CL) with S subset of Z+ and S circle plus NZ+=S for some N is an element of N . Some examples are also provided to illustrate our results.
The Krein-Milman Theorem is stated and proved in the general context of topological modules over topological ordered rings.
Let T be a bounded linear operator on a complex Hilbert space H. We say that T intertwines two bounded linear operators A and B on H if TA = BT. In particular, T is called supraposinormal if T intertwines QT star and T star P , for some positive operators Q and P, where at least one of P or Q has a dense range. In this work, we investigate when the product of two bounded linear operators on H remains supraposinormal. We illustrate our results with concrete examples. Finally, we characterize the supraposinormility of T using the properties of absolute values and square roots of positive operators.
A boundary value problem is considered for an X-valued Laplace equation, where X is a Hilbert space. The considered problem has specific features: the solution is sought in an X-valued Sobolev space; the boundary conditions are nonlocal in nature; the boundary conditions of the corresponding spectral problem are regular, but not strongly regular in the sense of Birkhoff. To solve this problem, we use the concept of a t-basis generated by the tensor product Lp(0,pi)circle times X . The spectral problem possesses two series of asymptotically close eigenfunctions, which therefore do not form a basis in Lp(0,1) . We construct a linear combination of eigenfunctions and establish the t-basisness of the resulting system for Lp([0,pi];X) . Using this fact, we prove the unique solvability of the BVP in Sobelev space Wp2(D;X) , where D=(0,1)& times;(0,pi) . We also emphasize that the results obtained are new even in the scalar-valued case.
In this paper, we develop a systematic theory based on Bell polynomials for evaluating parametric Ap & eacute;ry-type series. More specifically, starting from known series expansions involving central binomial coefficients, we establish connections between parametric Ap & eacute;ry-type series and beta-type integrals or generalized log-sine integrals. By applying several lemmas involving Bell polynomials to these special integrals and using properties of polygamma function and other special functions, we calculate these integrals and, consequently, the corresponding Ap & eacute;ry-type series. By specifying the parameters, we obtain evaluations for many special cases of such Ap & eacute;ry-type series.
In this paper, the main goal is to provide necessary and sufficient conditions for the Spanne- and Adams-type boundedness of parabolic fractional integral operator $ I_{\alpha }<^>{P} $ I alpha P in parabolic total Morrey-Guliyev spaces $ L_{p,\lambda,\mu }<^>{P}({\mathbb {R}<^>n}) $ Lp,lambda,mu P(Rn).
In this paper, we begin by defining finite versions of the digamma and cotangent functions, and examine their Laurent or power series expansions at integer points within a certain range. By constructing contour integrals involving these finite digamma and finite cotangent functions and performing residue calculations, we derive parity results for a finite version of the double polylogarithm function. Simply taking a limit then yields the known parity formulas satisfied by cyclotomic double zeta values.
In this paper, we obtain the necessary and sufficient conditions for the boundedness of integral operators commuting with dilations and rotations on the Cesaro space Ces(p)(R-n) (1 < p < infinity) when the kernels of these operators are nonnegative. In addition, the corresponding operator norms are also given. As applications, we derive the sharp estimates for the Hardy operator, the Hilbert operator and the Hardy-Littlewood fractional operator on Cesaro spaces.
