Related papers: Sampling theorem associated with q-Dirac system
As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces…
We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.
We derive a $q$-analogue of the matrix sixth Painlev\'e system via a connection-preserving deformation of a certain Fuchsian linear $q$-difference system. In specifying the linear $q$-difference system, we utilize the correspondence between…
We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete…
In this paper, we introduce q,{\omega}-Dirac system. We investigate the existence and uniqueness of solutions for this system and obtain some spectral properties based on the Hahn difference operator. Also we give two examples, which…
We introduce a q-analogue of the Peano kernel theorem by replacing ordinary derivatives and integrals by quantum derivatives and quantum integrals. In the limit q \to 1, the q-Peano kernel reduces to the classical Peano kernel. We also give…
In this article, after introducing a kind of q-deformation in quantum mechanics, first, q-deformed form of Dirac equation in relativistic quantum mechanics is derived. Then three important scat erring problem in physics are studied. All…
In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for…
We present a characterization of sets for which Cartwright's theorem holds true. The connection is discussed between these sets and sampling sets for entire functions of exponential type.
Digital signal theory is an extension of the analysis of continuous signals. This extension is provided by discretization and sampling. The sampling of signals can be mathematically described by a series of Dirac impulses and is well known.…
We present sampling theorems for reproducing kernel Banach spaces on Lie groups. Recent approaches to this problem rely on integrability of the kernel and its local oscillations. In this paper we replace the integrability conditions by…
This paper extends the Birman-Wenzl category by including a spin representation and then developing the recoupling theory, following Cvitanovic. In particular this gives a q-analogue of the chromatic evaluation of a spin network. The…
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables.…
A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid.
In our earlier work math.QA/9808015 some results on integral representations of functions in quantum disc were announced. It was then shown in math.QA/9808037 that the validity of those results is related to the invariance of kernels of…
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group $G$. Two main ideas from the classical theory having natural…
Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…