Related papers: On a correspondence between regular and non-regula…
Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…
Within this research, two combinatorial bijections using Young diagrams were studied. The first is a special case of a bijective correspondence between two classes of combinatorial objects. Its proof, based on Young diagrams, establishes…
We characterize disjoint hypercyclic sequences of wedge operators. Also, we give some sufficient conditions for a sequence of the dual wedge operators to be disjoint topologically transitive. Finally, we give some concrete examples and…
We give bijective results between several variants of lattice paths of length $2n$ (or $2n-2$) and integer compositions of n, all enumerated by the seemingly innocuous formula $4^{n-1}$. These associations lead us to make new connections…
In this paper, we give two explicit examples of unbounded linear maximal monotone operators. The first unbounded linear maximal monotone operator $S$ on $\ell^{2}$ is skew. We show its domain is a proper subset of the domain of its adjoint…
For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection we classify thick…
In this paper we extend Korovkin's theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function spaces. Several examples illustrating the theory are included.
This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.
In this paper, we investigate the algebras of consequence operators and finite consequence operators on a fixed language. Significant new collections of consequence operators are defined and shown to be complete and distributive…
$V$ denotes arbitrary bounded bijection on Hilbert space $H$. We try to describe the sets of $V$-stable vectors, i.e. the set of elements $x$ of $H$ such that the sequence $\|V^N x\| (N=1,2,...)$ is bounded (we also consider some other…
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
It is well known that there are entire functions whose orbit approximates any other entire function under the action of a sequence of translation operators . This result also holds for an uncountable family of sequences of translation…
We prove comparison principles for nonlinear potential theories in euclidian spaces in a very straightforward manner from duality and monotonicity. We shall also show how to deduce comparison principles for nonlinear differential operators,…
In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all…
Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
In the present paper we study stability of recurrence equations (which in particular case contain a dynamics of rational functions) generated by contractive functions defined on an arbitrary non-Archimedean algebra. Moreover,…