scholarly journals A Modified Analytic Function Space Feynman Integral and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Seung Jun Chang ◽  
Jae Gil Choi ◽  
Hyun Soo Chung
Keyword(s):  
Analytic Function ◽  
Function Space ◽  
Feynman Integral ◽  
Integration Formulas ◽  
Generalized Analytic Function ◽  
Analytic Function Space

We analyze the generalized analytic function space Feynman integral and then defined a modified generalized analytic function space Feynman integral to explain the physical circumstances. Integration formulas involving the modified generalized analytic function space Feynman integral are established which can be applied to several classes of functionals.

scholarly journals The Universal Teichmüller Space and Function Space

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yutong Liu ◽  
Yi Qi
Keyword(s):  
Analytic Function ◽  
Function Space ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Universal Teichmüller Space ◽  
And Function ◽  
Analytic Function Space

In this paper, a subspace TF02,1−s,s of the universal Teichmüller space, which is related to the analytic function space F02,1−s,s, is introduced and the holomorphy of the Bers map is shown. It is also proved that the pre-Bers map is holomorphic and the prelogarithmic derivative model T˜F02,1−s,s of TF02,1−s,s is a disconnected subset of the function space F02,1−s,s. Moreover, several equivalent descriptions of elements of TF02,1−s,s are obtained and the holomorphy of higher Bers maps is proved.

scholarly journals Composition operators on Qp spaces

2001 ◽  
Vol 70 (2) ◽  
pp. 161-188 ◽  
Author(s):  
Zengjian Lou
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Function Space ◽  
Composition Operators ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Holomorphic Functions ◽  
Bloch Spaces ◽  
Holomorphic Map ◽  
Analytic Function Space

AbstractA holomorphic map ψ of the unit disk ito itself induces an operator Cψ on holomorphic functions by composition. We characterize bounded and compact composition operators Cψ on Qp spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of Cψ from analytic function space X to Qp spaces, X = Dirichlet space D, Bloch space B or B0 = {f: f′ ∈ H∞}.

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.

The divisor of a generalized analytic function

1997 ◽  
Vol 61 (5) ◽  
pp. 547-552
Author(s):  
S. A. Grigoryan
Keyword(s):  
Analytic Function ◽  
Generalized Analytic Function

scholarly journals CONDITIONAL FEYNMAN INTEGRAL AND SCHRÖDINGER INTEGRAL EQUATION ON A FUNCTION SPACE

2009 ◽  
Vol 79 (1) ◽  
pp. 1-22 ◽  
Author(s):  
DONG HYUN CHO
Keyword(s):  
Integral Equation ◽  
Function Space ◽  
Feynman Integral ◽  
Borel Measures ◽  
Analytic Feynman Integral ◽  
Conditional Expectations ◽  
Image Position ◽  
Vector Valued ◽  
Complex Borel Measures ◽  
Stieltjes Transforms

AbstractLet Cr[0,t] be the function space of the vector-valued continuous paths x:[0,t]→ℝr and define Xt:Cr[0,t]→ℝ(n+1)r by Xt(x)=(x(0),x(t1),…,x(tn)), where 0<t1<⋯<tn=t. In this paper, using a simple formula for the conditional expectations of the functions on Cr[0,t] given Xt, we evaluate the conditional analytic Feynman integral Eanfq[Ft∣Xt] of Ft given by where θ(s,⋅) are the Fourier–Stieltjes transforms of the complex Borel measures on ℝr, and provide an inversion formula for Eanfq[Ft∣Xt]. Then we present an existence theorem for the solution of an integral equation including the integral equation which is formally equivalent to the Schrödinger differential equation. We show that the solution can be expressed by Eanfq[Ft∣Xt] and a probability distribution on ℝr when Xt(x)=(x(0),x(t)).

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

2020 ◽  
Author(s):  
Young Sik Kim
Keyword(s):  
Function Space ◽  
Partial Derivative ◽  
Feynman Integral ◽  
Wiener Integral ◽  
Analytic Feynman Integral ◽  
Change Of Scale

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

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