Related papers: q-convolution and its q-Fourier transform
Tsallis' q-Fourier transform is not generally one-to-one. It is shown here that, if we eliminate the requirement that $q$ be fixed, and let it instead "float", a simple extension of the $F_q-$definition, this procedure restores the…
In this paper we construct a q-analogue of the Legendre transformation, where q is a matrix of formal variables defining the phase space braidings between the coordinates and momenta (the extensive and intensive thermodynamic observables).…
It is shown that if the Fourier transform is a bounded map on a rearrangement-invariant space of functions on $\mathbb R^n$, modified by a weight, then the weight is bounded above and below and the space is equivalent to $L^2$. Also, if it…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal…
We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and…
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…
We explore a number of functional properties of the $q$-gamma function and a class of its quotients; including the $q$-beta function. We obtain formulas for all higher logarithmic derivatives of these quotients and give precise conditions…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
The classical Fourier transform on the line sends the operator of multiplication by $x$ to $i\frac{d}{d\xi}$ and the operator of differentiation $\frac{d}{d x}$ to the multiplication by $-i\xi$. For the Fourier transform on the Lobachevsky…
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set,…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
A q-deformed two-dimensional phase space is studied as a model for a noncommutative phase space. A lattice structure arises that can be interpreted as a spontaneous breaking of a continuous symmetry. The eigenfunctions of a Hamiltonian that…
We produce, on general homogeneous groups, an analogue of the usual H\"ormander pseudodifferential calculus on Euclidean space, at least as far as products and adjoints are concerned. In contrast to earlier works, we do not limit ourselves…
The q-difference analog of the classical ladder operators is derived for those orthogonal polynomials arising from a class of indeterminate moments problem.
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…
For a complete lattice $L$ and a relational structure $\mathfrak{X}=(X,(R_i)_I)$, we introduce the convolution algebra $L^{\mathfrak{X}}$. This algebra consists of the lattice $L^X$ equipped with an additional $n_i$-ary operation $f_i$ for…
Some q-analogues of classical integral transforms have recently been investigated by many authors in diverse citations. The q-analogues of the Natural transform are not known nor used. In the present paper, we are concerned with definitions…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
The strong dual space of linear continuous functionals on a weighted space G of infinitely differentiable functions defined on the real line is described in terms of their Fourier-Laplace transforms.