Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

The mutual consistency of boundary conditions twisted by an automorphism group G of the chiral algebra is studied for general modular invariants of rational conformal field theories. We show that a consistent set of twisted boundary states associated with any modular invariant realizes a non-negative integer matrix representation (NIM-rep) of the generalized fusion algebra, an extension of the ...

We construct the general supersymmetry algebra via the adjoint action on a semi-Hopf algebra which has a more general structure than a Hopf algebra. As a result we have an extended supersymmetry theory with quantum gauge group, i.e., quantised enveloping algebra of a simple Lie algebra. For the example, we construct the N =1 and generalized N =2 supersymmetry theory which leads to the Seiberg-W...

Starting with a spectral triple on unital C⁎-algebra A an action of discrete group G, if the is uniformly bounded (in Lipschitz sense) reduced crossed product A⋊rG constructed in [23]. The main instrument Kasparov external product. We note that this construction still works for twisted products when appropriate sense. Under suitable assumptions we discuss some basic properties resulting triples...

A well known and important theorem of analysis states that a function f(x) which is continuous on a bounded closed set E can be extended to the entire space, preserving its continuity. Let us consider a metric space S and a function f(x) defined and possessing a property P on a subset E of S. We shall for the sake of brevity say that ƒ (x) can be extended to S preserving property P , if there e...

We present the algebraic framework for the quantization of the classical bosonic charge algebra of maximally extended (N = 16) supergravity in two dimensions, thereby taking the first steps towards an exact quantization of this model. At the core of our construction is the Yangian algebra Y (e8) whose RTT presentation we discuss in detail. The full symmetry algebra is a centrally extended twist...

All Lie bialgebra structures for the (1+ 1)-dimensional centrally extended Schrödinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family of Schrödinger Poisson–Lie groups can be deduced by means of the Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended Galilei and g...

Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion of any abstract algebra is the extended Stone dual space of the Boolean algebra of recognisable subsets of the abstract algebra endowed with certain residuat...

Curado and Rego-Monteiro introduced in [2] a new algebraic structure generalizing the Heisenberg algebra and containing also the q-deformed oscillator as a particular case. This algebra, called generalized Heisenberg algebra, depends on an analytical function f and the eigenvalues αn of the Hamiltonian are given by the one-step recurrence αn+1 = f(αn). This structure has been used in different ...