Related papers: Star exponential functions as two-valued elements
In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…
We show that the eigenvalues and eigenfunctions of the stargenvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonian. Our method makes use of a Weyl-type representation of the…
In this note, we mainly consider the extended Weyl algebra of two generators (u,v), that is, the algebra generated by u,v with the fundamental commutation relation. Weyl algebra is realized on the space of polynomials of u and v by defining…
Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that $\frac{1}{i\h}uv$ in the Weyl algebra is naturally viewed as an…
This is a noncommutative version of the previous work entitled "Deformation Expression for Elements of Algebras (I)." In general in a noncommutative algebra, there is no canonical way to express elements in univalent way, which is often…
We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering where coordinates stand to the left…
In a noncommutative algebra there is no canonical way to express elements in univalent way, which is often called "ordering problem". In this note we give product formula of the Weyl algebra in generic ordered expression. In particular, the…
Using the formalism of quantizers and dequantizers, we show that the characters of irreducible unitary representations of finite and compact groups provide kernels for star products of complex-valued functions of the group elements.…
We establish the quaternionic weighted zeta function of a graph and its Study determinant expressions. For a graph with quaternionic weights on arcs, we define a zeta function by using an infinite product which is regarded as the Euler…
We show that various properties of unipotent elements in a reductive group over the complex numbers can be recovered purely in terms of the affine Weyl group of the dual group.
We construct a general quantization procedure for square integrable functions on well-behaved connected exponential Lie groups. The Lie groups in question should admit at least one co-adjoint orbit of maximal possible dimension. The…
We introduce a total order and the absolute value function for dual numbers. The absolute value function of dual numbers are with dual number values, and have properties similar to the properties of the absolute value function of real…
In this article we apply the duality technique of R. Howe to study the structure of the Weyl algebra. We introduce a one-parameter family of ``ordering maps'', where by an ordering map we understand a vector space isomorphism of the…
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
We study the space of vector valued theta functions for the Weil representation of a positive definite even lattice of rank two with fundamental discriminant. We work out the relation of this space to the corresponding scalar valued theta…
We show that positive elements with respect to the twisted convolutions, belonging to some ultra-test function space of certain order at origin, belong to the ultra-test function space of the same order everywhere. We apply the result to…
The theory of Weil-Stark elements is used to develop an axiomatic approach to the formulation of refined versions of Stark's Conjecture. This gives concrete new results concerning leading terms of Artin $L$-series and arithmetic properties…
We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class…
This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.
We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise…