Related papers: Infinite-Dimensional Bicomplex Hilbert Spaces
The quantum systems with finite-dimensional Hilbert space have several applications and are intensively explored theoretically and experimentally. The mathematical description of these systems follows the analogy with the usual…
A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert…
This is a survey on a notion of invariant operators, or Fourier multipliers on Hilbert spaces. This concept is defined with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. In particular this…
We set up a descriptive set-theoretic framework to study Lipschitz-free spaces and use the reduction argument of Bossard to prove several results. We prove two universality results: if a separable Banach space is isomorphically universal…
In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…
Representation theory of the quantum torus Hopf algebra, when the parameter $q$ is a root of unity, is studied. We investigate a decomposition map of the tensor product of two irreducibles into the direct sum of irreducibles, realized as a…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
We extend the Ax-Katz theorem for a single polynomial from finite fields to the rings Z_m with m composite. This extension not only yields the analogous result, but gives significantly higher divisibility bounds. We conjecture what computer…
It is often inevitable to introduce an indefinite-metric space in quantum field theory. There is a problem to determine the metric structure of a given representation space of field operators. We show the systematic method to determine such…
We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…
We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…
We develop a theory of weights for a quantum analogue of the symmetric pair (gl4,gl2 x gl2) realised as a quantum symmetric pair subalgebra. Based on Letzter's triangular decomposition we define Verma modules. Using magical operators that…
We start with observing that the only connected finite dimensional algebras with finitely many isomorphism classes of indecomposable bimodules are the quotients of the path algebras of uniformly oriented $A_n$-quivers modulo the radical…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
A powerful tool for studying geometrical problems in Hilbert space is developed. In particular, we study the quantum pure state tomography problem in finite dimensions from the point of view of dynamical systems and bifurcations theory.…
A classical result of Norbert Wiener characterises doubly shift-invariant subspaces for square integrable functions on the unit circle with respect to a finite positive Borel measure $\mu$, as being the ranges of the multiplication maps…
We study the representation theory of quantizations of Gieseker moduli spaces. We describe the categories of finite dimensional representations for all parameters and categories O for special values of parameters. We find the values of…
This treatise investigates holomorphic functions defined on the space of bicomplex numbers introduced by Segre. The theory of these functions is associated with Fueter's theory of regular, quaternionic functions. The algebras of quaternions…