Related papers: Nullstellens\"atze and Applications
We consider the class of non-commutative *-algebras which are path algebras of doubles of quivers with the natural involutions. We study the problem of extending positive truncated functionals on such *-algebras. An analog of the solution…
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-known Hilbert space case (where it coincides with the…
This paper offers a new and complete description of subnormal solutions of certain non-homogeneous second order periodic linear differential equations first studied by Gundersen and Steinbart in 1994. We have established a previously…
We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well-known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger's results a…
We introduce the concept of centrally algebraically closed division rings and show that a division ring satisfies the central Nullstellensatz if and only if it is centrally algebraically closed. We also show that every division ring can be…
In this article, we discuss some applications of the well-known Douglas factorization lemma in the context of von Neumann algebras. Let $\mathcal{B}(\mathscr{H})$ denote the set of bounded operators on a complex Hilbert space $\mathscr{H}$,…
The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and…
We prove a general archimedean positivstellensatz for hermitian operator-valued polynomials and show that it implies the multivariate Fejer-Riesz Theorem of Dritschel-Rovnyak and positivstellens\"atze of Ambrozie-Vasilescu and Scherer-Hol.…
We present a comparison between the performance of solvers based on Nystr\"om discretizations of several well-posed boundary integral equation formulations of Helmholtz transmission problems in two-dimensional Lipschitz domains.…
We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed by A. Seidenberg but no complete solution was…
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting…
In this paper an equation means a homogeneous linear partial differential equation in $n$ unknown functions of $m$ variables which has real or complex polynomial coefficients. The solution set consists of all $n$-tuples of real or complex…
In this paper, we present a computer-assisted framework for constructive proofs of existence for stationary solutions to one-dimensional parabolic PDEs and the rigorous determination of their linear stability. By expanding solutions in…
This is a translation of a final paper. It contains proofs of some well-known Positivstellens\"atze. The approach in this paper differs in two respects from presentations in literature. We use the Stone-Weierstrass Theorem directly to prove…
We prove a HVZ theorem for a general class of no-pair Hamiltonians describing an atom or positively charged ion with several electrons in the presence of a classical external magnetic field. Moreover, we show that there exist infinitely…
We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Z_k of order k. We then demonstrate how such a chain map induces a "Z_k-combinatorial Stokes theorem", which in turn…
The "openness" of a complex polynomial mapping is discussed and applied to the Fundamental Theorem of Algebra. In this category fall proofs of S. Wolfenstein, R.L. Thompson, J. Milnor, and S. Reich-S. Smale. These proofs take into account…
In this article, we use the Combinatorial Nullstellensatz to give new proofs of the Cauchy-Davenport, the Dias da Silva-Hamidoune and to generalize a previous addition theorem of the author. Precisely, this last result proves that for a set…
We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear…
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…