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Characterizations of the Solution Sets of Generalized Convex Minimization Problems

Ivanov, Vsevolod (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.In this paper we obtain some simple characterizations of the solution sets of a pseudoconvex program and a variational inequality. Similar characterizations of the solution set of a quasiconvex quadratic program are derived. Applications of these characterizations are given.

Characterizations of weakly compact sets and new fixed point free maps in c₀

P. N. Dowling, C. J. Lennard, B. Turett (2003)

Studia Mathematica

We give a basic sequence characterization of relative weak compactness in c₀ and we construct new examples of closed, bounded, convex subsets of c₀ failing the fixed point property for nonexpansive self-maps. Combining these results, we derive the following characterization of weak compactness for closed, bounded, convex subsets C of c₀: such a C is weakly compact if and only if all of its closed, convex, nonempty subsets have the fixed point property for nonexpansive mappings.

Characterizing Fréchet-Schwartz spaces via power bounded operators

Angela A. Albanese, José Bonet, Werner J. Ricker (2014)

Studia Mathematica

We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on them. This complements similar known characterizations of reflexive and of Fréchet-Montel spaces with a basis. Every strongly convergent sequence of continuous linear operators on a Fréchet-Schwartz space does so in a special way. We single out this type of "rapid convergence" for a sequence...

Characterizing spectra of closed operators through existence of slowly growing solutions of their Cauchy problems

Sen Huang (1995)

Studia Mathematica

Let A be a closed linear operator in a Banach space E. In the study of the nth-order abstract Cauchy problem u ( n ) ( t ) = A u ( t ) , t ∈ ℝ, one is led to considering the linear Volterra equation (AVE) u ( t ) = p ( t ) + A ʃ 0 t a ( t - s ) u ( s ) d s , t ∈ ℝ, where a ( · ) ∈ L l o c 1 ( ℝ ) and p(·) is a vector-valued polynomial of the form p ( t ) = ∑ j = 0 n 1 / ( j ! ) x j t j for some elements x j ∈ E . We describe the spectral properties of the operator A through the existence of slowly growing solutions of the (AVE). The main tool is the notion of Carleman spectrum of a vector-valued function. Moreover, an extension of a theorem...

Charge transfer scatteringin a constant electric field

Lech Zieliński (1999)

Colloquium Mathematicae

We prove the asymptotic completeness of the quantum scattering for a Stark Hamiltonian with a time dependent interaction potential, created by N classical particles moving in a constant electric field.

Cheeger inequalities for unbounded graph Laplacians

Frank Bauer, Matthias Keller, Radosław K. Wojciechowski (2015)

Journal of the European Mathematical Society

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.

Circular operators related to some quantum observables

Wacław Szymański (1997)

Annales Polonici Mathematici

Circular operators related to the operator of multiplication by a homomorphism of a locally compact abelian group and its restrictions are completely characterized. As particular cases descriptions of circular operators related to various quantum observables are given.

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