Search results for " function"
showing 10 items of 9395 documents
VECTOR MEASURES WITH VARIATION IN A BANACH FUNCTION SPACE
2003
Let E be a Banach function space and X be an arbitrary Banach space. Denote by E(X) the Kothe-Bochner function space defined as the set of measurable functions f : Ω → X such that the nonnegative functions ‖f‖X : Ω → [0,∞) are in the lattice E. The notion of E-variation of a measure —which allows to recover the pvariation (for E = Lp), Φ-variation (for E = LΦ) and the general notion introduced by Gresky and Uhl— is introduced. The space of measures of bounded E-variation VE(X) is then studied. It is shown, among other things and with some restriction of absolute continuity of the norms, that (E(X))∗ = VE′ (X ∗), that VE(X) can be identified with space of cone absolutely summing operators fr…
Generalized ``transition probability''
1975
An operationally meaningful symmetric function defined on pairs of states of an arbitrary physical system is constructed and is shown to coincide with the usual “transition probability” in the special case of systems admitting a quantum-mechanical description. It can be used to define a metric in the set of physical states. Conceivable applications to the analysis of certain aspects of Quantum Mechanics and to its possible modifications are mentioned.
Representable linear functionals on partial *-algebras
2012
A GNS-like *-representation of a partial *-algebra \({{\mathfrak A}}\) defined by certain representable linear functionals on \({{\mathfrak A}}\) is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.
Symmetry-assisted adversaries for quantum state generation
2011
We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target quantum states. There has been hope for quite some time that quantum state generation might be a route to tackle the $backslash$sc Graph Isomorphism problem. We show that for the related problem of $backslash$sc Index Erasure our method leads to a lower bound of $backslash Omega(backslash sqrt N)$ which matches an upper bound obtained via reduction to quantum search on $N$ elements. This closes an open problem first raised by Shi [FOCS'02]. Our approach is …
Geometric Properties of Planar BV -Extension Domains
2009
We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.
On the conical density properties of measures on $\mathbb{R}^n$
2005
We compare conical density properties and spherical density properties for general Borel measures on $\mathbb{R}^n$ . As a consequence, we obtain results for packing and Hausdorff measures $\mathcal{P}_h$ and $\mathcal{H}_h$ provided that the gauge function $h$ satisfies certain conditions. One consequence of our general results is the following: let $m, n\,{\in}\,\mathbb{N}, 0\,{\lt}\,s\,{\lt}\,m\,{\leq}\,n$ , $0\,{\lt}\,\eta\,{\lt}\,1$ , and suppose that $V$ is an $m$ -dimensional linear subspace of $\mathbb{R}^n$ . Let $\mu$ be either the $s$ -dimensional Hausdorff measure or the $s$ -dimensional packing measure restricted to a set $A$ with $\mu(A)\,{\lt}\,\infty$ . Then for $\mu$ -almos…
Learning with confidence
1996
Herein we investigate learning in the limit where confidence in the current conjecture accrues with time. Confidence levels are given by rational numbers between 0 and 1. The traditional requirement that for learning in the limit is that a device must converge (in the limit) to a correct answer. We further demand that the associated confidence in the answer (monotonically) approach 1 in the limit. In addition to being a more realistic model of learning, our new notion turns out to be a more powerful as well. In addition, we give precise characterizations of the classes of functions that are learnable in our new model(s).
Enumeration of L-convex polyominoes by rows and columns
2005
In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.
Efficient algorithm for learning simple regular expressions from noisy examples
1994
We present an efficient algorithm for finding approximate repetitions in a given sequence of characters. First, we define a class of simple regular expressions which are of star-height one and do not contain union operations, and a stochastic mutation process of a given length over a string of characters. Then, assuming that a given string of characters is obtained corrupted by the defined mutation process from some long enough word generated by a simple regular expression, we try to restore the expression. We prove that to within some reasonable accuracy it is always possible if the length of the mutation process is bounded comparing to the length of the example. We provide an algorithm by…
Cluster values of holomorphic functions of bounded type
2015
We study the cluster value theorem for Hb(X), the Fréchet algebra of holomorphic functions bounded on bounded sets of X. We also describe the (size of) fibers of the spectrum of Hb(X). Our results are rather complete whenever X has an unconditional shrinking basis and for X = ℓ1. As a byproduct, we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of ℓ1. Fil: Aron, Richard Martin. Kent State University; Estados Unidos Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina Fil: Lassalle, S…