相关论文: Generalized raising and lowering operators for sup…
The Schrodinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in…
We apply recent knowledge and techniques of the new generalized upper and lower Legendre conjugates to the theory of weight functions in the sense of Braun-Meise-Taylor and study in detail the effects on the corresponding associated weight…
We develop an operator algebraic framework for generalized Cardano polynomials and show how their structure naturally leads to an operator formulation of Cardano method that is compatible with tools and concepts from quantum information…
We introduce a class of multidimensional Schr\"odinger operators with elliptic potential which generalize the classical Lam\'e operator to higher dimensions. One natural example is the Calogero--Moser operator, others are related to the…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
We generalize classical orthogonalization procedures from real linear algebra to the setting of fermionic quantum (FQ) operations. In the case of the Gram-Schmidt orthogonalization procedure, the generalization is easy. This, however, helps…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
The coefficients occurring in summation formulae of the Lubbock type are shown to be generalised Bernoulli polynomials which turn up in subdivision questions such as quantum field theory around a conical singularity and on spherical lunes.…
A generalization of the generating function for Gegenbauer polynomials is introduced whose coefficients are given in terms of associated Legendre functions of the second kind. We discuss how our expansion represents a generalization of…
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…
The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
We present a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In its standard form, the quantum volume operator is constructed from tetrahedra whose faces are endowed with…
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum,…
Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to define convolution structures and modulus of smoothness for…
A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the…
We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in…