scholarly journals Wiener integral for the coordinate process under theσ-finite measure unifying Brownian penalisations

2010 ◽  
Vol 15 ◽  
pp. S69-S84
Author(s):  
Kouji Yano
Keyword(s):  
Finite Measure ◽  
Wiener Integral ◽  
Coordinate Process

On the Integrability of the Ergodic Hilbert Transform for A Class of Functions with Equal Absolute Values

1998 ◽  
Vol 5 (2) ◽  
pp. 101-106
Author(s):  
L. Ephremidze
Keyword(s):  
Hilbert Transform ◽  
Measure Space ◽  
Integrable Function ◽  
Finite Measure ◽  
Ergodic Transformation ◽  
Finite Measure Space ◽  
Class Of Functions

Abstract It is proved that for an arbitrary non-atomic finite measure space with a measure-preserving ergodic transformation there exists an integrable function f such that the ergodic Hilbert transform of any function equal in absolute values to f is non-integrable.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

Induced transformations of recurrent a.m.s. dynamical systems

2015 ◽  
Vol 15 (02) ◽  
pp. 1550010
Author(s):  
Sheng Huang ◽  
Mikael Skoglund
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Random Process ◽  
Ergodic Theorem ◽  
Finite Measure ◽  
Stationary Random Process ◽  
Finite State ◽  
Ratio Ergodic Theorem

This note proves that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon–McMillan–Breiman theorem, as well as the Shannon–McMillan theorem, holds for all reduced processes of any finite-state recurrent asymptotically mean stationary random process. As a by-product, a ratio ergodic theorem for asymptotically mean stationary dynamical systems is presented.

A remarkable σ-finite measure on related to many Brownian penalisations

2007 ◽  
Vol 345 (8) ◽  
pp. 459-466 ◽  
Author(s):  
Joseph Najnudel ◽  
Bernard Roynette ◽  
Marc Yor
Keyword(s):  
Finite Measure

scholarly journals A Partial Derivative Approach to the Change of Scale Formula for the Function Space Integral

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 26
Author(s):  
Young Sik Kim
Keyword(s):  
Fourier Transform ◽  
Function Space ◽  
Partial Derivative ◽  
Directional Derivative ◽  
Feynman Integral ◽  
Wiener Integral ◽  
Vector Calculus ◽  
Change Of Scale

We investigate the partial derivative approach to the change of scale formula for the functon space integral and we investigate the vector calculus approach to the directional derivative on the function space and prove relationships among the Wiener integral and the Feynman integral about the directional derivative of a Fourier transform.

scholarly journals Periodically and quasi-periodically driven dynamics of Bose-Einstein condensates

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Pengfei Zhang ◽  
Yingfei Gu
Keyword(s):  
Phase Boundary ◽  
Quantum Dynamics ◽  
Scattering Length ◽  
Finite Measure ◽  
Sine Wave ◽  
Square Wave ◽  
Periodically Driven ◽  
Two Phases ◽  
Almost All ◽  
Bose Einstein

We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

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