scholarly journals Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions

2013 ◽  
Vol 142 (3) ◽  
pp. 1075-1087 ◽  
Author(s):  
J. A. Jaramillo ◽  
M. Jiménez-Sevilla ◽  
L. Sánchez-González
Keyword(s):  
Finsler Manifold ◽  
Smooth Functions

The d-plane radon transform on the torus $$ \mathbb{T}^n $$

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Ahmed Abouelaz
Keyword(s):  
Radon Transform ◽  
Inversion Formula ◽  
Flat Torus ◽  
Smooth Functions ◽  
Suitable Function

AbstractWe define and study the d-plane Radon transform, namely R, on the n-dimensional (flat) torus. The transformation R is obtained by integrating a suitable function f over all d-dimensional geodesics (d-planes in the torus). We specially establish an explicit inversion formula of R and we give a characterization of the image, under the d-plane Radon transform, of the space of smooth functions on the torus.

scholarly journals Differential-free Characterisation of Smooth Mappings with Controlled Growth

2018 ◽  
Vol 61 (3) ◽  
pp. 628-636 ◽  
Author(s):  
Marijan Marković
Keyword(s):  
Unit Ball ◽  
Bloch Space ◽  
Controlled Growth ◽  
Smooth Functions

AbstractIn this paper we give some generalizations and improvements of the Pavlović result on the Holland–Walsh type characterization of the Bloch space of continuously differentiable (smooth) functions in the unit ball in Rm.

scholarly journals Characterization of traces of smooth functions on Ahlfors regular sets

2013 ◽  
Vol 265 (9) ◽  
pp. 1870-1915 ◽  
Author(s):  
Lizaveta Ihnatsyeva ◽  
Antti V. Vähäkangas
Keyword(s):  
Smooth Functions ◽  
Regular Sets

DUAL GEOMETRY OF THE WIGNER–YANASE–DYSON INFORMATION CONTENT

2003 ◽  
Vol 06 (03) ◽  
pp. 413-430 ◽  
Author(s):  
HIROSHI HASEGAWA
Keyword(s):  
Affine Connection ◽  
Smooth Functions ◽  
Finite Dimensional ◽  
Skew Information ◽  
Quantum Version ◽  
Characterizing Function ◽  
Matrix Manifolds ◽  
Stochastic Mapping ◽  
Identification Theorem

We develop a non-parametric information geometry on finite-dimensional matrix manifolds by using the Fréchet differentiation. Taking the simplest prototype Riemannian metric form [Formula: see text], [Formula: see text] with the Fréchet derivative D on a pair of smooth functions g(ρ) and g*(ρ) of the density matrix ρ, we prove the WYD identification theorem: this metric is identified with the normalized Wigner–Yanase–Dyson skew information (the WYD metric), if and only if the metric form satisfies the monotonicity under every stochastic mapping T on ρ and A: [Formula: see text]. On this basis, we establish (a) a fine structure of the partial order in the set ℱ of all monotone metrics such that ℱ power ∪ℱ WYD forms a linearly ordered subset of ℱ with the same mini-max bound, where ℱ power (the power-mean metrics) interpolates the Bures and the WYD metrics (b) a characterization of the quasi-entropy S (ρ, σ)= Tr F (Δσ, ρ)ρ induced by the metric-characterizing function f WYD (x) of the WYD metric (c) an affine connection on the above metric which is torsionless to guarantee the quantum version of the ±α-connection, provided α∈[-3, 3].

scholarly journals PTOLEMAIC SPACES AND CAT(0)

2009 ◽  
Vol 51 (2) ◽  
pp. 301-314 ◽  
Author(s):  
S. M. BUCKLEY ◽  
K. FALK ◽  
D. J. WRAITH
Keyword(s):  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Metric Space ◽  
Metric Spaces ◽  
Finsler Manifold ◽  
Full Generality ◽  
Space Setting ◽  
Ptolemaic Space

AbstractWe consider Ptolemy's inequality in a metric space setting. It is not hard to see that CAT(0) spaces satisfy this inequality. Although the converse is not true in full generality, we show that if our Ptolemaic space is either a Riemannian or Finsler manifold, then it must also be CAT(0). Ptolemy's inequality is closely related to inversions of metric spaces. We exploit this link to establish a new characterization of Euclidean space amongst all Riemannian manifolds.

Concircularity on GRW-space-times and conformally flat spaces

2021 ◽  
pp. 2150132
Author(s):  
Sharief Deshmukh ◽  
Ibrahim Al-Dayel
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Potential Function ◽  
Lorentzian Manifold ◽  
Momentum Tensor ◽  
Conformally Flat ◽  
Smooth Functions ◽  
Necessary And Sufficient ◽  
Flat Riemannian Manifold

There are two smooth functions [Formula: see text] and [Formula: see text] associated to a nontrivial concircular vector field [Formula: see text] on a connected Riemannian manifold [Formula: see text], called potential function and connecting function. In this paper, we show that presence of a timelike nontrivial concircular vector field influences the geometry of generalized Robertson–Walker space-times. We use a timelike concircular vector field [Formula: see text] on an [Formula: see text] -dimensional connected conformally flat Lorentzian manifold, [Formula: see text], to find a characterization of generalized Robertson–Walker space-time with  fibers Einstein manifolds. It is interesting to note that for [Formula: see text] the concircular vector field annihilates energy-momentum tensor and also that in this case the potential function [Formula: see text] is harmonic. In the second part of this paper, we show that presence of a nontrivial concircular vector field [Formula: see text] with connecting function [Formula: see text] on a complete and connected [Formula: see text] -dimensional conformally flat Riemannian manifold [Formula: see text], [Formula: see text], with Ricci curvature [Formula: see text] non-negative, satisfying [Formula: see text], is necessary and sufficient for [Formula: see text] to be isometric to either a sphere [Formula: see text] or to the Euclidean space [Formula: see text], where [Formula: see text] is the scalar curvature.

scholarly journals Smooth Approximation of Lipschitz Functions on Finsler Manifolds

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. I. Garrido ◽  
J. A. Jaramillo ◽  
Y. C. Rangel
Keyword(s):  
Lipschitz Function ◽  
Composition Operators ◽  
Lipschitz Functions ◽  
Finsler Manifold ◽  
Positive Continuous Function ◽  
Smooth Approximation ◽  
Finsler Manifolds ◽  
Lipschitz Constants ◽  
Bounded Derivative

We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz functionf:M→ℝdefined on a connected, second countable Finsler manifoldM, for each positive continuous functionε:M→(0,∞)and eachr>0, there exists aC1-smooth Lipschitz functiong:M→ℝsuch that|f(x)-g(x)|≤ε(x), for everyx∈M, andLip(g)≤Lip(f)+r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebraCb1(M)of allC1functions with bounded derivative on a complete quasi-reversible Finsler manifoldM, we obtain a characterization of algebra isomorphismsT:Cb1(N)→Cb1(M)as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.

scholarly journals Characterization of merged AIRS and MLS water vapor sensitivity through integration of averaging kernels and retrievals

2010 ◽  
Vol 3 (4) ◽  
pp. 2833-2859 ◽  
Author(s):  
C. K. Liang ◽  
A. Eldering ◽  
F. W. Irion ◽  
W. G. Read ◽  
E. J. Fetzer ◽  
...  
Keyword(s):  
Water Vapor ◽  
Temperature Scale ◽  
Scale Height ◽  
Atmospheric Infrared Sounder ◽  
High Quality ◽  
Smooth Functions ◽  
Upper Troposphere ◽  
Atmospheric State

Abstract. In this paper, we analyze averaging kernels to assess the sensitivity of the Aqua Atmospheric Infrared Sounder (AIRS) and Aura Microwave Limb Sounder (MLS) to water vapor. The averaging kernels, in the tropical and extra-tropical upper tropospheric and lower stratospheric region of the atmosphere, indicate that AIRS is primarily sensitive to water vapor concentrations typical of tropospheric values up to a level around 260 hPa. At lower pressures AIRS retrievals lose sensitivity to water vapor, though not completely as indicated by the non-zero verticalities at pressures less than 260 hPa. The MLS is able to provide high quality retrievals, with verticalities ~1 for all pressure levels, down to the same level for where AIRS begins to lose sensitivity. Previous analyses have estimated both instruments to have overlapping sensitivity to water vapor over a half temperature scale height layer, within the upper troposphere, for concentrations between ~30–400 ppmv. Thus, we implement a method using the averaging kernel information to join the AIRS and MLS profiles into an merged set of water vapor profiles. The final combined profiles are not only smooth functions with height but preserve the atmospheric state as interpreted by both the AIRS and MLS instruments.

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