Related papers: Hilbert space for quantum mechanics on superspace

This article describes Hilbert spaces contractively contained in certain reproducing kernel Hilbert spaces of analytic functions on the open unit disc which are nearly invariant under division by an inner function. We extend Hitt's theorem…

Let $\mathbb{H}$ be a separable Hilbert space. In this paper we establish a generalization of Walnut's representation and Janssen's representation of the $\mathbb{H}-$valued Gabor frame operator on $\mathbb{H}-$valued weighted amalgam…

In this paper, we shall consider the notion of bicomplex inner product and define bicomplex Hilbert space. We shall define $L^{2}[a,b]$ where the functions take bicomplex values. We shall prove the Theorem for a bounded self adjoint…

A definition of frames for Krein spaces is proposed, which extends the notion of $J$-orthonormal basis of Krein spaces. A $J$-frame for a Krein space $(\HH, \K{\,}{\,})$ is in particular a frame for $\HH$ in the Hilbert space sense. But it…

We generalize recent results in two-dimensional Jackiw-Teitelboim gravity to study factorization of the Hilbert space of eternal black holes in quantum gravity with a negative cosmological constant in any dimension. We approach the problem…

We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…

Let E_lambda be a Hilbert space, whose elements are functions spanned by the eigenfunctions of the Laplace-Beltrami operator associated with an eigenvalue lambda>0. The norm of elements in this space is given by the Petersson inner product.…

In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…

We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dimensional notion of a closed subspace of H. Orthocomplemented…

In this paper, we introduce the concept of inner product on weak hypervector spaces and prove some results about them.

This paper considers the construction of Reproducing Kernel Hilbert Spaces (RKHS) on the sphere as an alternative to the conventional Hilbert space using the inner product that yields the L^2(S^2) function space of finite energy signals. In…

In this work, it is demonstrated how the kinematical Hilbert space of Loop Quantum Gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined…

A classical theorem of Stone and von Neumann says that the Schr\"{o}dinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on…

Let $\Omega_n$ be the ring of polynomial-valued holomorphic differential forms on complex $n$-space, referred to in physics as the superspace ring of rank $n$. The symmetric group $\mathfrak{S}_n$ acts diagonally on $\Omega_n$ by permuting…

We provide a new general scheme for the geometric quantisation of $\operatorname{Sp}(1)$-symmetric hyper-K\"ahler manifolds, considering Hilbert spaces of holomorphic sections with respect to the complex structures in the hyper-K\"ahler…

We consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space of square integrable functions and the…

An array of N subsequent Laguerre polynomials is interpreted as an eigenvector of a non-Hermitian tridiagonal Hamiltonian $H$ with real spectrum or, better said, of an exactly solvable N-site-lattice cryptohermitian Hamiltonian whose…

In this paper, we study and classify Hilbert space representations of cross product *-algebras of the quantized enveloping algebra $U_q(e_2)$ with the coordinate algebras $O(E_q(2))$ of the quantum motion group and $O(\C_q)$ of the complex…

Let $M^n$ be either a simply connected space form or a rank-one symmetric space of noncompact type. We consider Weingarten hypersurfaces of $M\times\mathbb R$, which are those whose principal curvatures $k_1,\dots ,k_n$ and angle function…

We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type $G/K$ can be used for questions of solvability of systems of invariant differential equations in analogy to…