scholarly journals Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yessica Hernández-Eliseo ◽  
Josué Ramírez-Ortega ◽  
Francisco G. Hernández-Zamora
Keyword(s):  
Toeplitz Operators ◽  
Continuous Functions ◽  
Two Dimensional ◽  
Siegel Domain ◽  
Limit Values ◽  
Type Space ◽  
Measurable Functions ◽  
Finite Set ◽  
Type Spaces ◽  
Piecewise Continuous

We describe certain C ∗ -algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain D 2 ⊂ ℂ 2 . Bounded measurable functions of the form c Im   ζ 1 , Im   ζ 2 − ζ 1 2 are called nilpotent symbols. In this work, we consider symbols of the form a Im   ζ 1 b Im   ζ 2 − ζ 1 2 , where both limits lim s → 0 + b s and lim s → + ∞ b s exist, and a s belongs to the set of piecewise continuous functions on ℝ ¯ = − ∞ , + ∞ and having one-side limit values at each point of a finite set S ⊂ ℝ . We prove that the C ∗ -algebra generated by all Toeplitz operators T a b is isomorphic to C Π ¯ , where Π ¯ = ℝ ¯ × ℝ ¯ + and ℝ ¯ + = 0 , + ∞ .

scholarly journals On guarantee optimization in control problem with finite set of disturbances

2021 ◽  
Vol 31 (4) ◽  
pp. 613-628
Author(s):  
M.I. Gomoyunov ◽  
D.A. Serkov
Keyword(s):  
Control Problem ◽  
Control Strategies ◽  
Continuous Functions ◽  
Functional Constraint ◽  
Memory Strategies ◽  
Memory Strategy ◽  
Classical Formulation ◽  
Technical Assumption ◽  
Finite Set ◽  
Piecewise Continuous

In this paper, we deal with a control problem under conditions of disturbances, which is stated as a problem of optimization of the guaranteed result. Compared to the classical formulation of such problems, we assume that the set of admissible disturbances is finite and consists of piecewise continuous functions. In connection with this additional functional constraint on the disturbance, we introduce an appropriate class of non-anticipative control strategies and consider the corresponding value of the optimal guaranteed result. Under a technical assumption concerning a property of distinguishability of the admissible disturbances, we prove that this result can be achieved by using control strategies with full memory. As a consequence, we establish unimprovability of the class of full-memory strategies. A key element of the proof is a procedure of recovering the disturbance acting in the system, which allows us to associate every non-anticipative strategy with a full-memory strategy providing a close guaranteed result. The paper concludes with an illustrative example.

scholarly journals Improving KKM Theory on General Metric Type Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Sehie Park
Keyword(s):  
Convex Space ◽  
Metric Spaces ◽  
Space Theory ◽  
Type Space ◽  
Generalized Metric ◽  
Abstract Convex Space ◽  
Type Spaces

Abstract A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

scholarly journals On the topology of fuzzy metric type spaces

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 133-141 ◽  
Author(s):  
Reza Saadati
Keyword(s):  
Type Space ◽  
Fuzzy Metric ◽  
Type Spaces

In this paper, first we introduce the concept of fuzzy metric type space and consider the topology induced by a fuzzy metric type. Next, we consider the complete fuzzy metric type spaces and prove that any G? set in a complete metric type space is a complete fuzzy metrizable type space.

scholarly journals Toeplitz Operators on Dirichlet-Type Space of Unit Ball

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jin Xia ◽  
Xiaofeng Wang ◽  
Guangfu Cao
Keyword(s):  
Toeplitz Operator ◽  
Boundary Point ◽  
Toeplitz Operators ◽  
Radial Function ◽  
Type Space ◽  
Dirichlet Type ◽  
Algebraic Properties ◽  
Commuting Problem ◽  
Product Problem ◽  
Dirichlet Type Space

We construct a functionuinL2Bn, dVwhich is unbounded on any neighborhood of each boundary point ofBnsuch that Toeplitz operatorTuis a Schattenp-class0<p<∞operator on Dirichlet-type spaceDBn, dV. Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type spaceDBn, dV. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the formξkuis studied, wherek ∈ Zn,ξ ∈ ∂Bn, anduis a radial function.

A Reinforced Tabu Search Approach for 2D Strip Packing

2012 ◽  
pp. 171-188
Author(s):  
Giglia Gómez-Villouta ◽  
Jean-Philippe Hamiez ◽  
Jin-Kao Hao
Keyword(s):  
Tabu Search ◽  
Search Algorithm ◽  
Fitness Function ◽  
Packing Problem ◽  
Two Dimensional ◽  
Strip Packing ◽  
Benchmark Instances ◽  
Finite Set ◽  
Infinite Height ◽  
Search Approach

This paper discusses a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied considers regular items, rectangular to be precise, that must be packed without overlap, not allowing rotations. The objective is to minimize the height of the resulting packing. In this regard, the authors present a local search algorithm based on the well-known tabu search metaheuristic. Two important components of the presented tabu search strategy are reinforced in attempting to include problem knowledge. The fitness function incorporates a measure related to the empty spaces, while the diversification relies on a set of historically “frozen” objects. The resulting reinforced tabu search approach is evaluated on a set of well-known hard benchmark instances and compared with state-of-the-art algorithms.

scholarly journals Best Simultaneous approximation of quasi-continuous functions by monotone functions

1991 ◽  
Vol 50 (3) ◽  
pp. 391-408 ◽  
Author(s):  
Salem M. A. Sahab
Keyword(s):  
Banach Space ◽  
Convex Cone ◽  
Simultaneous Approximation ◽  
Continuous Functions ◽  
Unit Interval ◽  
Closed Convex Cone ◽  
Monotone Functions ◽  
Measurable Functions ◽  
Best Simultaneous Approximation ◽  
Nondecreasing Functions

AbstractLet Q denote the Banach space (under the sup norm) of quasi-continuous functions on the unit interval [0, 1]. Let ℳ denote the closed convex cone comprised of monotone nondecreasing functions on [0, 1]. For f and g in Q and 1 < p < ∞, let hp denote the best Lp-simultaneous approximant of f and g by elements of ℳ. It is shown that hp converges uniformly as p → ∞ to a best L∞-simultaneous approximant of f and g by elements of ℳ. However, this convergence is not true in general for any pair of bounded Lebesgue measurable functions. If f and g are continuous, then each hp is continuous; so is limp→∞ hp = h∞.

Note on an Application of the δ-Function in the Representation of Solutions of Algebraic Equations

1967 ◽  
Vol 10 (5) ◽  
pp. 735-738
Author(s):  
J. B. Sabat
Keyword(s):  
Continuous Function ◽  
Delta Function ◽  
Continuous Functions ◽  
Dirac Delta Function ◽  
Algebraic Equations ◽  
Dirac Delta ◽  
Representation Of Solutions ◽  
Piecewise Continuous ◽  
Image Position

The “function” δ(x - xo) is known as the Dirac Delta function and may be defined as zero everywhere except at xo, where it is infinite in such a way that1having property that for every continuous function φ(x) on (a, b)2It is well known [2] δ(x-xo) can be approximated as a limit of a sequence of piecewise continuous functions, and there is an abundance of such sequences.

Sign in / Sign up

Export Citation Format

Share Document