Search results for "Bounded"
showing 10 items of 658 documents
On the Minimal Solution of the Problem of Primitives
2000
Abstract We characterize the primitives of the minimal extension of the Lebesgue integral which also integrates the derivatives of differentiable functions (called the C -integral). Then we prove that each BV function is a multiplier for the C -integral and that the product of a derivative and a BV function is a derivative modulo a Lebesgue integrable function having arbitrarily small L 1 -norm.
Homomorphisms between Algebras of Holomorphic Functions
2014
For two complex Banach spaces X and Y, in this paper, we study the generalized spectrum M-b(X,Y) of all nonzero algebra homomorphisms from H-b(X), the algebra of all bounded type entire functions on X into H-b(Y). We endow M-b(X,Y) with a structure of Riemann domain over L(X*,Y*) whenever.. is symmetrically regular. The size of the fibers is also studied. Following the philosophy of ( Aron et al., 1991), this is a step to study the set M-b,M-infinity (X,B-Y) of all nonzero algebra homomorphisms from Hb(b) (X) into H-infinity (B-Y) of bounded holomorphic functions on the open unit ball of Y and M-infinity(B-X,B-Y) of all nonzero algebra homomorphisms from H-infinity(B-X) into H infinity (B-Y…
The Bergman projection on weighted spaces: L1and Herz spaces
2002
We nd necessary and sucien t conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli{Rudin are bounded on L 1 (w) and in the Herz spaces K q(w). 1. Introduction and preliminaries. The purpose of this paper is to study spaces of analytic functions on the unit disc D provided with a norm of a weighted Herz space. More precisely we consider the classical family of Bergman projections Ps, s > 1, and we give necessary and sucien t conditions on the weight making these projections continuous in the cor- responding weighted Herz space. We also consider the continuity of these
CQ*-Algebras of Operators and Application to Quantum Models
2000
C*-algebras constitute, as known, the cornerstones of the Haag-Kastler [1] algebraic approach to quantum systems, with infinitely many degrees of freedom: one usually starts, in fact, with associating to each bounded region V of the configuration space of the system the C*-algebra A v of local observables in V. The uniform completion A of the algebra A0 generated by the Av’s is then considered as the C*-algebra of observables of the system.
Rectifiability and analytic capacity in the complex plane
1995
Analytic capacity and removable sets In this chapter we shall discuss a classical problem in complex analysis and its relations to the rectifiability of sets in the complex plane C . The problem is the following: which compact sets E ⊃ C are removable for bounded analytic functions in the following sense? (19.1) If U is an open set in C containing E and f : U\E → C is a bounded analytic function, then f has an analytic extension to U . This problem has been studied for almost a century, but a geometric characterization of such removable sets is still lacking. We shall prove some partial results and discuss some other results and conjectures. For many different function classes a complete so…
Existence and almost uniqueness for p -harmonic Green functions on bounded domains in metric spaces
2020
We study ($p$-harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive capacity, and that they satisfy very precise capacitary identities for superlevel sets. Suitably normalized singular functions are called Green functions. Uniqueness of Green functions is largely an open problem beyond unweighted $\mathbf{R}^n$, but we show that all Green functions (in a given domain and with the same singularity) are comparable. As a consequence, for $p$-harmonic functions with a given pole we obtain a similar comparison result near the pole. Various c…
Discontinuous, although “highly” differentiable, real functions and algebraic genericity
2021
Abstract We exhibit a class of functions f : R → R which are bounded, continuous on R ∖ Q , left discontinuous on Q , right differentiable on Q , and upper left Dini differentiable on R ∖ Q . Other properties of these functions, such as jump sizes and local extrema, are also discussed. These functions are constructed using probabilistic methods. We also show that the families of functions satisfying similar properties contain large algebraic structures (obtaining lineability, algebrability and coneability).
Quasi *-algebras of measurable operators
2009
Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra $(\X,\Ao)$ possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.
Weak commutation relations of unbounded operators: Nonlinear extensions
2013
We continue our analysis of the consequences of the commutation relation $[S,T]=\Id$, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations.
Hilbert-Schmidt Hankel operators on the Segal-Bargmann space
2004
This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions onCn\mathbb {C}^nthat are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbolg∈L∞(Cn)g \in L^{\infty }(\mathbb {C}^n)the Hankel operatorHgH_gis of the Hilbert-Schmidt class if and only ifHg¯H_{\bar {g}}is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operatorsHgH_gandHg¯H_{\bar {g}}coincide. But, in general, if we deal with bounded symbols, only the inequality‖Hg‖HS≤2‖Hg¯‖HS\|H_g\|_{HS}\leq 2\|H_{\bar {g}}\|_{HS}can be proved. The resul…