SUFFICIENT CONDITIONS FOR INTERPOLATION AND SAMPLING HYPERSURFACES IN THE BERGMAN BALL

2007 ◽  
Vol 18 (05) ◽  
pp. 559-584 ◽  
Author(s):  
TAMÁS FORGÁCS ◽  
DROR VAROLIN
Keyword(s):  
Recent Work ◽  
Fock Space ◽  
Sufficient Conditions ◽  
Higher Dimensions ◽  
Sampling Theorem ◽  
Interpolation Theorem ◽  
Smooth Hypersurface ◽  
Present Setting ◽  
Geometric Density ◽  
Natural Method

We give sufficient conditions for a closed smooth hypersurface W in the n-dimensional Bergman ball to be interpolating or sampling. As in the recent work [5] of Ortega-Cerdà, Schuster and the second author on the Bargmann–Fock space, our sufficient conditions are expressed in terms of a geometric density of the hypersurface that, though less natural, is shown to be equivalent to Bergman ball analogs of the Beurling-type densities used in [5]. In the interpolation theorem we interpolate L2 data from W to the ball using the method of Ohsawa–Takegoshi, extended to the present setting, rather than the Cousin I approach used in [5]. In the sampling theorem, our proof is completely different from [5]. We adapt the more natural method of Berndtsson and Ortega-Cerdà [1] to higher dimensions. This adaptation motivated the notion of density that we introduced. The approaches of [5] and the present paper both work in either the case of the Bergman ball or of the Bargmann–Fock space.

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

scholarly journals Interpolation and sampling hypersurfaces for the Bargmann-Fock space in higher dimensions

2006 ◽  
Vol 335 (1) ◽  
pp. 79-107 ◽  
Author(s):  
Joaquim Ortega-Cerdà ◽  
Alexander Schuster ◽  
Dror Varolin
Keyword(s):  
Fock Space ◽  
Higher Dimensions

Asymptotic stability of heteroclinic cycles in systems with symmetry

1995 ◽  
Vol 15 (1) ◽  
pp. 121-147 ◽  
Author(s):  
Martin Krupa ◽  
Ian Melbourne
Keyword(s):  
Asymptotic Stability ◽  
Ad Hoc ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Higher Dimensions ◽  
Systematic Investigation ◽  
Heteroclinic Cycles ◽  
General Sufficient Condition ◽  
Higher Dimensional ◽  
The Stability

AbstractSystems possessing symmetries often admit heteroclinic cycles that persist under perturbations that respect the symmetry. The asymptotic stability of such cycles has previously been studied on an ad hoc basis by many authors. Sufficient conditions, but usually not necessary conditions, for the stability of these cycles have been obtained via a variety of different techniques.We begin a systematic investigation into the asymptotic stability of such cycles. A general sufficient condition for asymptotic stability is obtained, together with algebraic criteria for deciding when this condition is also necessary. These criteria are always satisfied in ℝ3 and often satisfied in higher dimensions. We end by applying our results to several higher-dimensional examples that occur in mode interactions with O(2) symmetry.

scholarly journals Two Sufficient Conditions for Convex Ordering on Risk Aggregation

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Dan Zhu ◽  
Chuancun Yin
Keyword(s):  
Sufficient Conditions ◽  
Higher Dimensions ◽  
Stochastic Orders ◽  
Weak Correlation ◽  
Convex Ordering ◽  
Risk Aggregation ◽  
Dependent Risks ◽  
Stop Loss

We define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with the same marginals. Moreover, some properties and relations of stochastic orders are discussed.

scholarly journals Convergence theorems of a scheme for I-asymptotically quasi-nonexpansive type mapping in Banach space

2015 ◽  
Vol 97 (111) ◽  
pp. 239-251
Author(s):  
Seyit Temir
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Recent Work ◽  
Nonempty Subset ◽  
Sufficient Conditions ◽  
Convergence Theorems ◽  
Type Mapping ◽  
Necessary And Sufficient

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K ? K be an I-asymptotically quasi-nonexpansive type mapping and I : K ? K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type mappping in Banach spaces to a common fixed point of T and I. Also, we study the convergence of the Ishikawa iterative sequences to common fixed point for nonself I-asymptotically quasinonexpansive type mapping in Banach spaces. The results presented in this paper extend and generalize some recent work of Chang and Zhou [1], Wang [19], Yao and Wang [20] and many others.

On Packings of Unequal Spheres in Rn

1968 ◽  
Vol 20 ◽  
pp. 967-969 ◽  
Author(s):  
D. G. Larman
Keyword(s):  
Lower Bound ◽  
Recent Work ◽  
Higher Dimensions ◽  
Unit Cube ◽  
Two Dimensions

Suppose that a sequence of spheres is packed in order of decreasing diameters into the unit cube In of Rn. In recent work (2), I have shown that for n = 2, there exist positive constants K2, s ( = 0.97) such that the area of has an asymptotic lower bound K2(d(Sm))s. Although the methods used were complicated and possibly only viable in two dimensions, it is intuitively clear that such a result should also be true in higher dimensions.

Gaussian Quantum Markov Semigroups on a One-Mode Fock Space: Irreducibility and Normal Invariant States

2021 ◽  
Vol 28 (01) ◽  
pp. 2150001
Author(s):  
J. Agredo ◽  
F. Fagnola ◽  
D. Poletti
Keyword(s):  
Existence And Uniqueness ◽  
Fock Space ◽  
Sufficient Conditions ◽  
Quantum Oscillator ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Type Condition ◽  
Invariant States ◽  
Quantum Markov Semigroup ◽  
Necessary And Sufficient

We consider the most general Gaussian quantum Markov semigroup on a one-mode Fock space, discuss its construction from the generalized GKSL representation of the generator. We prove the known explicit formula on Weyl operators, characterize irreducibility and its equivalence to a Hörmander type condition on commutators and establish necessary and sufficient conditions for existence and uniqueness of normal invariant states. We illustrate these results by applications to the open quantum oscillator and the quantum Fokker-Planck model.

scholarly journals Univalence criteria for a general integral operator

2021 ◽  
Vol 37 (1) ◽  
pp. 23-33
Author(s):  
CAMELIA BARBATU ◽  
DANIEL BREAZ
Keyword(s):  
Integral Operator ◽  
Recent Work ◽  
Sufficient Conditions ◽  
Open Disk ◽  
General Integral ◽  
General Integral Operator ◽  
Univalence Criteria

"The main object of this paper is to give sufficient conditions for the general integral operator Tn, to be univalent in the open disk U, when gi, hi, ki ∈ Gbi for all i = 1, n. This general integral operator was considered in a recent work [Barbatu, C. and Breaz, D., ˘ Classes of an univalent integral operator, Studia Univ. Babes¸-Bolyai Math., accepted]. The results derived in this paper are shown to follow upon specializing the parameters involved in our results. Several corollaries of the main results are also considered."

scholarly journals Multidimensional Iterative Filtering Method for the Decomposition of High–Dimensional Non–Stationary Signals

2017 ◽  
Vol 10 (2) ◽  
pp. 278-298 ◽  
Author(s):  
Antonio Cicone ◽  
Haomin Zhou
Keyword(s):  
Sufficient Conditions ◽  
Higher Dimensions ◽  
High Dimensional ◽  
Alternative Technique ◽  
Time Frequency ◽  
Filtering Method ◽  
Convergence Results ◽  
Mode Decomposition ◽  
Stationary Signals ◽  
Iterative Filtering

AbstractIterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non–stationary and non–linear signals. Recently in [3] IF has been proved to be convergent for anyL2signal and its stability has been also demonstrated through examples. Furthermore in [3] the so called Fokker–Planck (FP) filters have been introduced. They are smooth at every point and have compact supports. Based on those results, in this paper we introduce the Multidimensional Iterative Filtering (MIF) technique for the decomposition and time–frequency analysis of non–stationary high–dimensional signals. We present the extension of FP filters to higher dimensions. We prove convergence results under general sufficient conditions on the filter shape. Finally we illustrate the promising performance of MIF algorithm, equipped with high–dimensional FP filters, when applied to the decomposition of two dimensional signals.

Sign in / Sign up

Export Citation Format

Share Document