Related papers: Theorem of completeness for a Dirac-type operator …
An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant…
In these notes we first review Pauli's proof of his `fundamental theorem' that states the equivalence of any two sets of Dirac matrices $\{ \gamma^\mu \}$. Due to this theorem not only all physical results in the context of the Dirac…
We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…
We consider the wave equation with a distributional Dirac damping and Dirichlet boundary conditions on a compact interval. It is shown that the spectrum of the corresponding wave operator is fully determined by zeroes of an entire function.…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
Sufficient conditions for a discrete spectrum of the biharmonic equation in a two-dimensional peak-shaped domain are established. Different boundary conditions from Kirchhoff's plate theory are imposed on the boundary and the results depend…
We derive sufficient conditions for theories consisting of multiple vector fields, which could also couple to external fields, to be multi-field generalised Proca theories. The conditions are derived by demanding that the theories have the…
Our main result (Theorem A) shows the incompleteness of any consistent sequential theory T formulated in a finite language such that T is axiomatized by a collection of sentences of bounded quantifier-alternation-depth. Our proof employs an…
An operator set is functionally incomplete if it can not represent the full set $\lbrace \neg,\vee,\wedge,\rightarrow,\leftrightarrow\rbrace$. The verification for the functional incompleteness highly relies on constructive proofs. The…
Abstract. In this work we derive a sufficient condition to ensure certain genus 0 entire function that can have only negative zeros. We also apply this result to the Riemann hypothesis and generalized Riemann hypothesis for some primitive…
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axioms, besides the Kuratowski closure axioms, are a `product…
In [17], we obtained the spectral Einstein functional associated with the Dirac operator for n-dimensional manifolds without boundary. In this paper, we give the proof of general Dabrowski-Sitarz-Zalecki type theorems for the spectral…
The paper is concerned with the completeness problem of root functions of general boundary value problems for first order systems of ordinary differential equations. Namely, we introduce and investigate the class of \emph{weakly regular…
A particular consequence of the famous Carleson-Hunt theorem is that the Taylor series expansions of bounded holomorphic functions on the open unit disk converge almost everywhere on the boundary, whereas on single points the convergence…
We prove a topological completeness theorem for the modal logic GLP containing operators $\langle\lambda\rangle$ for $\lambda \in$ Ord intended to capture progressively stronger notions of consistency in mathematical theories. We show that,…
In this paper we give necessary and sufficient conditions for a bounded linear operator $T$ to be generalized Drazin-Riesz invertible or generalized Drazin-meromorphic invertible. Also, we study generalized Browder's theorem and generalized…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
We generalize previous results and demonstrate that the Dirac representation theory can be effectively adjusted and applied to continuous or discrete signals of infinite time duration. The role of the identity and projection operators is…
Given a compact interval $I \subseteq \mathbb{R}$, and a function $f$ that is a product of a nonzero polynomial with a Gaussian, it will be shown that the translates $\{ f(\cdot - \lambda) : \lambda \in \Lambda \}$ are complete in $C(I)$ if…
We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model $\mathcal A$ of a computably enumerable, model complete theory, the…