Search results for "rete"

On the regularity of the partial {$O\sp *$}-algebras generated by a closed symmetric operator

1992

Let be given a dense domain D in a Hilbert space and a closed symmetric operator T with domain containing D. Then the restriction of T to D generates (algebraically) two partial *-algebras of closable operators (called weak and strong), possibly nonabelian and nonassociative. We characterize them completely. In particular, we examine under what conditions they are regular, that is, consist of polynomials only, and standard. Simple differential operators provide concrete examples of all the pathologies allowed by the abstract theory.

Isometries between spaces of weighted holomorphic functions

2009

A result of Suzuki type in partial G-metric spaces

2014

Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial …

Multi-valued F-contractions and the solution of certain functional and integral equations

2013

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

Automatic continuity of generalized local linear operators

1980

In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.

Quasihyperbolic boundary conditions and Poincaré domains

2002

We prove that a domain in ${\Bbb R}^n$ whose quasihyperbolic metric satisfies a logarithmic growth condition with coefficient $\beta\le 1$ is a (q,p)-\Poincare domain for all p and q satisfying $p\in[1,\infty)\cap(n-n\beta,n)$ and $q\in[p,\beta p^*)$ , where $p^*=np/(n-p)$ denotes the Sobolev conjugate exponent. An elementary example shows that the given ranges for p and q are sharp. The proof makes use of estimates for a variational capacity. When p=2 we give an application to the solvability of the Neumann problem on domains with irregular boundaries. We also discuss the relationship between this growth condition on the quasihyperbolic metric and the s-John condition.

Eine Bemerkung zum Normenresthomomorphismus $h : K_{\ast} F/2 \longrightarrow H^{\ast} (F, \mathbb{Z}/2)$

2003

An elementary Galois theoretic proof is given for the fact: An element $b \in \dot{F}$ is a norm from the extension $F (\sqrt{a})$ iff $(a) \cup (b) = 0$ in $H^{2} (F, \mathbb{Z}/2)$. From this it follows easily that h exists. Comments about other proofs and applications to quadratic forms conclude the paper.

Quasi-conformal mapping theorem and bifurcations

1998

LetH be a germ of holomorphic diffeomorphism at 0 ∈ ℂ. Using the existence theorem for quasi-conformal mappings, it is possible to prove that there exists a multivalued germS at 0, such thatS(ze 2πi )=H○S(z) (1). IfH λ is an unfolding of diffeomorphisms depending on λ ∈ (ℂ,0), withH 0=Id, one introduces its ideal $$\mathcal{I}_H$$ . It is the ideal generated by the germs of coefficients (a i (λ), 0) at 0 ∈ ℂ k , whereH λ(z)−z=Σa i (λ)z i . Then one can find a parameter solutionS λ (z) of (1) which has at each pointz 0 belonging to the domain of definition ofS 0, an expansion in seriesS λ(z)=z+Σb i (λ)(z−z 0) i with $$(b_i ,0) \in \mathcal{I}_H$$ , for alli. This result may be applied to the…

ISOMETRY GROUPS OF WEIGHTED SPACES OF HOLOMORPHIC FUNCTIONS: TRANSITIVITY AND UNIQUENESS

2009

We survey some recent results on the isometries of weighted spaces of holomorphic functions defined on an open subset of ℂn. We will see that these isometries are determined by a subgroup of the automorphisms on a distinguished subset of the domain. We will look for weights with 'large' groups of isometries and observe that in certain circumstances the group of isometries determines the weight.

Decomposability in the space ofHKP-integrable functions

2014

In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.