Related papers: Functional determinants on certain domains
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
In this paper, we find several determinants expressing the Fibonomial coefficients. We also give the generating functions, Vandermonde identity, and continued fractions about Fibonomial coefficients.
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
We explicitly describe the divisor class groups and semidualizing modules for ladder determinantal rings with coefficients in an arbitrary normal domain for arbitrary ladders, not necessarily connected, and all sizes of minors.
A fixed point result is given for a class of functional contractions over local Branciari metric spaces. It extends some contributions in the area due to Fora et al [Mat. Vesnik, 61 (2009), 203-208].
The zeta function associated with higher-spin fields on the Euclidean $4$-ball is investigated. The leading coefficients of the corresponding heat-kernel expansion are given explicitly and the zeta functional determinant is calculated. For…
We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of…
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
The propagation of scalar and spinor fields in a spacetime whose metric changes signature is analyzed. Recent work of Dray et al. on particle production from signature change for a (massless) scalar field is reviewed, and an attempt is made…
We study the geometry and partial differential equations arising from the consideration of Frobenius determinants, also called-group-determinants. This leads us to address some aspects of twistor theory as well as some extensions of Bessel…
We explicitly give factorization formulas for higher depth determinants, which are defined via derivatives of the spectral zeta function at non-positive integer points, of Laplacians on the n-sphere in terms of the multiple gamma functions.
Within the scope of a spherically symmetric space-time we study the role of a nonlinear spinor field in the formation of different configurations with spherical symmetries. The presence of the non-diagonal components of energy-momentum…
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate…
An almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. Also, an almost periodic function in…
In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…
We consider scalar and spinor particles in the spacetime of a domain wall in the context of low energy effective string theories, such as the generalized scalar-tensor gravity theories. This class of theories allows for an arbitrary…
We prove that the homological and Balmer spectra in tensor-triangular geometry are functorial in certain definable functors, thereby providing an alternative perspective on functoriality in tensor-triangular geometry from the viewpoint of…
The dynamics of cosmic scalar fields with flat potential is studied. Their contribution to the expansion rate of the universe is analyzed, and their behaviour in a simple model of phase transitions is discussed.
In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.
In this article, we give all the Weitzenb\"ock-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit…