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A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic manifolds. Both, time-independent and time-dependent dynamics…
The complete knowledge of a theory is encoded in its correlation functions. Thus non-perturbative effects, like confinement in QCD, is necessarily contained in these correlation functions. As a consequence, a number of confinement scenarios…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
In this paper we investigate the problems related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier-Stieltjes transform). Since it is known that the set of all such measures does not have a…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
The link between the scaling function extracted from the analysis of (e,e') cross sections and the spectral function/momentum distribution in nuclei is revisited. Several descriptions of the spectral function based on the independent…
We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.
This paper is an electronic application to my set of lectures, subject:`Formal methods in solving differential equations and constructing models of physical phenomena'. Addressed, mainly: postgraduates and related readers. Content: a…
We study the Carath\'{e}odory and Kobayashi metrics by way of the method of dual extremal problems in functional analysis. Particularly incisive results are obtained for convex domains.
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
A general approach for derivation of the spectral relations for the multitime correlation functions is presented. A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
In this paper, some existence results for sign-changing critical points of locally Lipschitz functionals in real Banach space are obtained by the method combining the invariant sets of descending ow method with a quantitative deformation.…
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse…
We consider the Carrollian conformal field theories involving scalar operators in the momentum representation. The momentum space Ward identities are explicitly solved to obtain the different branches of 2 and 3 point Carrollian conformal…
In the framework of the signal processing approach to single-atom resonance fluorescence with spectral resolution, we diagrammatically derive an analytical formula for arbitrary-order spectral correlation functions of the scattered fields…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
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…