Related papers: Linear canonical space-time transform and convolut…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
Canonical quantization of quantum field theory models is inherently related to the Lorentz invariant partition of classical fields into the positive and the negative frequency parts $u(x) = u^+(x) + u^-(x),$ performed with the help of…
A canonical transformation of a new type is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum…
We introduce multilinear localization operators in terms of the short-time Fourier transform, and multilinear Weyl pseudodifferential operators. We prove that such localization operators are in fact Weyl pseudodifferential operators whose…
We analyze the recently proposed Spectral Quark Model in the light of Chiral Perturbation Theory in curved space-time. In particular, we calculate the chiral coefficients $L_1, ..., L_{10}$, as well as the coefficients $L_{11}$, $L_{12}$,…
A covariant description of the canonical theory for interacting classical fields is developed on a space-like hypersurface. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in…
The derivation of the transformations between inertial frames made by Mansouri and Sexl is generalised to three dimensions for an arbitrary direction of the velocity. Assuming lenght contraction and time dilation to have their relativistic…
This paper formulates a conjectural description of of the space of weightless functions (see\cite{BK}) and raises a question about a possibility of extending such a description in a more general context.
It is shown that a generic quadro-quartic Cremonian spacetime, which is endowed with one spatial and three time dimensions, can continuously evolve into a signature-reversed configuration, i.e. into the classical spacetime featuring one…
The short-time linear canonical transform (STLCT) can be identified as a generalization of the short-time Fourier transform (STFT). It is a novel time-frequency analysis tool. In this paper, we generalize some different uncertainty…
It is shown that performing simultaneously two transformations on functions of space and time (for instance a Fourier transform on the space variable and a Laplace transform on the time variable) can be easier than performing them one after…
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…
In conventional machine learning applications, each data attribute is assumed to be orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus there is no distinction of in-between relations of dimensions.…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship…
This note shows how to align a periodic signal with its the Fourier transform by means of frequency or time scaling. This may be useful in developing new algorithms, e.g. for pitch estimation. This note also convolves the signals and the…
We define an infinite class of unitary transformations between position and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian…
We develop a theory of pseudo-differential operators associated with the gyrator transform on modulation spaces. The gyrator transform is a two-dimensional linear canonical transform which can be viewed as a rotation in the time-frequency…
Being a powerful tool for linear time-invariant (LTI) systems, system response analysis can also be applied to the so-called linear space-invariant (LSI) but time-varying systems, which is a dual of the conventional LTI problems. In this…
A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above…