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Spectral theory and operator ergodic theory on super-reflexive Banach spaces

Earl Berkson (2010)

Studia Mathematica

On reflexive spaces trigonometrically well-bounded operators have an operator-ergodic-theory characterization as the invertible operators U such that s u p n ∈ ℕ , z ∈ | | ∑ 0 < | k | ≤ n ( 1 - | k | / ( n + 1 ) ) k - 1 z k U k | | < ∞ . (*) Trigonometrically well-bounded operators permeate many settings of modern analysis, and this note highlights the advances in both their spectral theory and operator ergodic theory made possible by a recent rekindling of interest in the R. C. James inequalities for super-reflexive spaces. When the James inequalities are combined with Young-Stieltjes...

Spline Subdivision Schemes for Compact Sets. A Survey

Dyn, Nira, Farkhi, Elza (2002)

Serdica Mathematical Journal

Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, IsraelAttempts at extending spline subdivision schemes to operate on compact sets are reviewed. The aim is to develop a procedure for approximating a set-valued function with compact images from a finite set of its samples. This is motivated by the problem of reconstructing a 3D object from...

Squaring a reverse AM-GM inequality

Minghua Lin (2013)

Studia Mathematica

Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.

Stability and Continuity of Functions of Least Gradient

H. Hakkarainen, R. Korte, P. Lahti, N. Shanmugalingam (2015)

Analysis and Geometry in Metric Spaces

In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.

Stability criteria of linear neutral systems with distributed delays

Guang-Da Hu (2011)

Kybernetika

In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded...

Standard ideals in convolution Sobolev algebras on the half-line

José E. Galé, Antoni Wawrzyńczyk (2011)

Colloquium Mathematicae

We study the relation between standard ideals of the convolution Sobolev algebra ₊ ( n ) ( t ⁿ ) and the convolution Beurling algebra L¹((1+t)ⁿ) on the half-line (0,∞). In particular it is proved that all closed ideals in ₊ ( n ) ( t ⁿ ) with compact and countable hull are standard.

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