scholarly journals A Lecture About the Use of Orlicz Spaces in Information Geometry

2021 ◽  
pp. 179-195
Author(s):  
Giovanni Pistone
Keyword(s):  
Orlicz Spaces ◽  
Information Geometry

scholarly journals Quantum Orlicz Spaces in Information Geometry

2004 ◽  
Vol 11 (04) ◽  
pp. 359-375 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Information ◽  
Tangent Space ◽  
Selfadjoint Operator ◽  
Affine Connection ◽  
Orlicz Spaces ◽  
Trace Class ◽  
Information Geometry ◽  
Young Function ◽  
Affine Structure ◽  
Cotangent Space

Let H0 be a selfadjoint operator such that Tr e−βH0 is of trace class for some β < 1, and let χɛ denote the set of ɛ-bounded forms, i.e., ∥(H0+C)−1/2−ɛX(H0+C)−1/2+ɛ∥ < C for some C > 0. Let χ := Span ∪ɛ∈(0,1/2]χɛ. Let [Formula: see text] denote the underlying set of the quantum information manifold of states of the form ρx = e−H0−X−ψx, X ∈ χ. We show that if Tr e−H0 = 1. 1. the map Φ, [Formula: see text] is a quantum Young function defined on χ 2. The Orlicz space defined by Φ is the tangent space of [Formula: see text] at ρ0; its affine structure is defined by the (+1)-connection of Amari 3. The subset of a ‘hood of ρ0, consisting of p-nearby states (those [Formula: see text] obeying C−1ρ1+p ≤ σ ≤ Cρ1 − p for some C > 1) admits a flat affine connection known as the (−1) connection, and the span of this set is part of the cotangent space of [Formula: see text] 4. These dual structures extend to the completions in the Luxemburg norms.

Calderón–Zygmund singular integrals in central Morrey–Orlicz spaces

2020 ◽  
Vol 72 (2) ◽  
pp. 235-259
Author(s):  
Lech Maligranda ◽  
Katsuo Matsuoka
Keyword(s):  
Singular Integrals ◽  
Orlicz Spaces

Martingale Rransforms between Hardy-Orlicz Spaces of LΦPredictable Martingales

2012 ◽  
Vol 14 (3) ◽  
pp. 245
Author(s):  
Feng LUO ◽  
Lin YU ◽  
Hongping GUO
Keyword(s):  
Orlicz Spaces

Müntz Rational Approximation in Orlicz Spaces

2012 ◽  
Vol 14 (1) ◽  
pp. 55
Author(s):  
Xiaohong WU ◽  
Garidi WU
Keyword(s):  
Rational Approximation ◽  
Orlicz Spaces

scholarly journals Optimal UAV Circumnavigation Control with Input Saturation Based on Information Geometry

2020 ◽  
Vol 53 (2) ◽  
pp. 2471-2476
Author(s):  
Yangguang Yu ◽  
Xiangke Wang ◽  
Lincheng Shen
Keyword(s):  
Input Saturation ◽  
Information Geometry

scholarly journals Information Geometry for Radar Target Detection with Total Jensen–Bregman Divergence

Entropy ◽  
2018 ◽  
Vol 20 (4) ◽  
pp. 256 ◽  
Author(s):  
Xiaoqiang Hua ◽  
Haiyan Fan ◽  
Yongqiang Cheng ◽  
Hongqiang Wang ◽  
Yuliang Qin
Keyword(s):  
Target Detection ◽  
Information Geometry ◽  
Bregman Divergence ◽  
Radar Target
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