Related papers: Titchmarsh theorem associated with QFT
In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
We study a class of anomalies associated with time-reversal and spatial reflection symmetry in (2+1)D topological phases of matter. In these systems, the topological quantum numbers of the quasiparticles, such as the fusion rules and…
Quantum analogues of the transient fluctuation theorem(TFT) and steady-state fluctuation theorem(SSFT) are investigated for a harmonic oscillator linearly coupled with a harmonic reservoir. The probability distribution for the work done…
In this note, we describe an interpretation of the (continuous) Fourier transform from the perspective of the Chinese Remainder Theorem. Some related issues, including a new derivation of Poisson summation formula, are discussed.
We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we…
We extend the equivalence of the Salem type for the Riemann hypothesis by application of Titchmarsh's theorem. Other equivalences to the Riemann hypothesis and notes on related Fourier integrals are provided.
We prove a formula relating the fermionic forms and the Poincare polynomials of quiver varieties associated to a finite quiver. Applied to quivers of type ADE, our result implies a version of the fermionic conjecture of Lusztig.
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
We treat equivariant completions of toric contraction morphisms as an application of the toric Mori theory. For this purpose, we generalize the toric Mori theory for non-$\mathbb Q$-factorial toric varieties. So, our theory seems to be…
We establish the equivalence between $U(1)$ Chern-Simons and Reshetikhin-Turaev TQFTs associated with finite quadratic modules. For gauge group $U(1)$ and even level $k$, we prove that the corresponding Chern-Simons TQFT is naturally…
The paper is devoted to the development of the octonion Fourier transform (OFT) theory initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization of earlier work by Blaszczyk and Snopek, where they proved…
The application of methods of time-dependent density functional theory (TDDFT) to systems of qubits provided the interesting possibility of simulating an assigned Hamiltonian evolution by means of an auxiliary Hamiltonian having different…
In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a quaternionic variable are established with the help of basis transformations of…
This paper is an introductory text to the theory of $q$-deformed Fourier transforms, as first discussed by Rogov and Olshanetsky. We derive the well-known results in detail, present them in a format that suits our needs, and include some…
We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive…
The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized…
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
We build a four-dimensional quaternion-parametrized conformal field theory (QCFT) using quaternion holomorphic functions as the generators of quaternionic conformal transformations. Taking the two-dimensional complex-parametrized conformal…
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…