Search results for " Integra"
showing 10 items of 2527 documents
Resolvent Estimates for Non-Selfadjoint Operators via Semigroups
2009
We consider a non-selfadjoint h-pseudodifferential operator P in the semiclassical limit (h → 0). If p is the leading symbol, then under suitable assumptions about the behavior of p at infinity, we know that the resolvent (z–P)–1 is uniformly bounded for z in any compact set not intersecting the closure of the range of p. Under a subellipticity condition, we show that the resolvent extends locally inside the range up to a distance \(\mathcal{O}(1)((h\ln \frac{1}{h})^{k/(k + 1)} )\) from certain boundary points, where \(k \in \{ 2,4, \ldots \} \). This is a slight improvement of a result by Dencker, Zworski, and the author, and it was recently obtained by W. Bordeaux Montrieux in a model sit…
Functional Calculus and Fredholm Criteria for Boundary Value Problems on Noncompact Manifolds
1992
A Boutet de Monvel type calculus is developed for boundary value problems on (possibly) noncompact manifolds. It is based on a class of weighted symbols and Sobolev spaces. If the underlying manifold is compact, one recovers the standard calculus. The following is proven:
Multiplicative Decompositions of Holomorphic Fredholm Functions and ψ*-Algebras
1999
In this article we construct multiplicative decompositions of holomorphic Fredholm operator valued functions on Stein manifolds with values in various algebras of differential and pseudo differential operators which are submultiplicative ψ* - algebras, a concept introduced by the first author. For Fredholm functions T(z) satisfying an obvious topological condition we. Prove (0.1) T(z) = A(z)(I + S(z)), where A(z) is holomorphic and invertible and S(z) is holomorphic with values in an “arbitrarily small” operator ideal. This is a stronger condition on S(z) than in the authors' additive decomposition theorem for meromorphic inverses of holomorphic Fredholm functions [12], where the smallness …
On a multiplication and a theory of integration for belief and plausibility functions
1987
Abstract Belief and plausibility functions have been introduced as generalizations of probability measures, which abandon the axiom of additivity. It turns out that elementwise multiplication is a binary operation on the set of belief functions. If the set functions of the type considered here are defined on a locally compact and separable space X , a theorem by Choquet ensures that they can be represented by a probability measure on the space containing the closed subsets of X , the so-called basic probability assignment. This is basic for defining two new types of integrals. One of them may be used to measure the degree of non-additivity of the belief or plausibility function. The other o…
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.
A Decomposition Theorem for the Fuzzy Henstock Integral
2012
We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.
On a normal form of symmetric maps of [0, 1]
1980
A class of continuous symmetric mappings of [0, 1] into itself is considered leaving invariant a measure absolutely continuous with respect to the Lebesgue measure.
Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces
1992
The pseudodifferential operators with symbols in the Grushin classes \~S inf0 supρ,δ , 0 ≤ δ < ρ ≤ 1, of slowly varying symbols are shown to form spectrally invariant unital Frecher-*-algebras (Ψ*-algebras) in L(L 2(R n )) and in L(H γ st ) for weighted Sobolev spaces H infγ sup defined via a weight d function γ. In all cases, the Fredholm property of an operator can be characterized by uniform ellipticity of the symbol. This gives a converse to theorems of Grushin and Kumano-Ta-Taniguchi. Both, the spectrum and the Fredholm spectrum of an operator turn out to be independent of the choices of s, t and γ. The characterization of the Fredholm property by uniform ellipticity leads to an index …
Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
2012
Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.
QCD sum rule calculation ofK ℓ3 form factors
1992
We present a combined finite energy sum rule (FESR) and analytic continuation by duality (ACD) calculation of the (neutral)K l3 decay. We confirm the Callan-Treiman relation and investigate the validity of a linear fit for the form factors. Furthermore, we obtain ζ=−0.1...−0.3, consistent with the mean experimental value ζ=−0.1±0.09.