Related papers: An Inverse Theorem for the Perron--Frobenius Theor…
We consider the question of, given operators $A$, $Z$ and a sequence of invertible operators $U_n\to Z$, whether the sequence $U_nAU_n^{-1}$ is bounded in norm, as well as generalizations of this where $U_nAU_n^{-1}$ is modified by some…
We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive $C_0$-semigroup on an $L^p$-space is strongly convergent in case that it has a strictly positive fixed point and contains an integral…
In this paper we study the operator inequality \phi(X)\leq X and the operator equation \phi(X)= X, where \phi is a w^*-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one…
Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…
The inverse conjecture for the Gowers norms $U^d(V)$ for finite-dimensional vector spaces $V$ over a finite field $\F$ asserts, roughly speaking, that a bounded function $f$ has large Gowers norm $\|f\|_{U^d(V)}$ if and only if it…
The Hamiltonian reggeon acting in Bargmann space is non-Hermitian with respect to the standard scalar product associated to Bargmann space. Hence the question arises, whether the eigenfunctions by the finite norm condition form a complete…
Given a finite set $X\subseteq\R$ we characterize the diagonals of self-adjoint operators with spectrum $X$. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to…
Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the…
We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space,…
In this paper, we establish the one-sided maximal ergodic inequalities for a large subclass of positive operators on noncommutative $L_p$-spaces for a fixed $1<p<\infty$, which particularly applies to positive isometries and general…
We prove that every bounded, positive, irreducible, stochastically continuous semigroup on the space of bounded, measurable functions which is strong Feller, consists of kernel operators and possesses an invariant measure converges…
The inverse problem, to reconstruct the general multivector wave function from the observable quadratic densities, is solved for 3D geometric algebra. It is found that operators which are applied to the right side of the wave function must…
We revise the strong convergent Chernoff product formula and extend it, in a Hilbert space, to convergence in the operator-norm topology. Main results deal with the self-adjoint Chernoff product formula. The nonself-adjoint case concerns…
We investigate the self-adjointness of the two dimensional Dirac operator with infinite mass boundary conditions on an unbounded domain with an infinite number of corners. We prove that if the domain has no concave corners, then the…
We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a…
We present a new theorem concerning a sufficient condition for a symmetric operator acting in a complex Hilbert space to be essentially self-adjoint. By applying the theorem, we prove that the Dirac Maxwell Hamiltonian, which describes a…
Let $A$ be a positive bounded linear operator on a complex Hilbert space $\mathcal{H}$ and $\mathcal{B}_{A}(\mathcal{H})$ be the subspace of all operators which admit $A$-adjoints operators. In this paper, we establish some inequalities…
Covering ill-posed problems with compact and non-compact operators regarding the degree of ill-posedness is a never ending story written by many authors in the inverse problems literature. This paper tries to add a new narrative and some…
The global homeomorphism theorem for quasiconformal maps describes the following specifically higher-dimensional phenomenon: {\em Locally invertible quasiconformal mapping $f: {\R}^{n} \to {\R}^{n}$ is globally invertible provided $n > 2$.}…
We show that a simplified version of the Dirac interaction operator given by $\hat H_\mathrm{I} \propto \int d\mathbf{k}d\mathbf{p}(\hat a(\mathbf{k}) + \hat a^\dagger(-\mathbf{k})) \hat b^\dagger(\mathbf{p} + \mathbf{k}) \hat…