Some relationships for the double modified generalized analytic function space Fourier-Feynman transform and its applications

2016 ◽  
Vol 290 (4) ◽  
pp. 520-533
Author(s):  
Seung Jun Chang ◽  
Jae Gil Choi ◽  
Hyun Soo Chung
Keyword(s):  
Analytic Function ◽  
Function Space ◽  
Generalized Analytic Function ◽  
Analytic Function Space

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∞}.

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

On the Use of POCS for Restoring the “Missing Wedge” in Electron Tomography

1990 ◽  
Vol 48 (1) ◽  
pp. 520-521
Author(s):  
Neng-Yu Zhang ◽  
Bruce F. McEwen ◽  
Joachim Frank
Keyword(s):  
Function Space ◽  
Convex Sets ◽  
Electron Tomography ◽  
Spinal Ganglion ◽  
Fourier Space ◽  
Missing Information ◽  
Voltage Electron ◽  
High Voltage Electron Microscope ◽  
Energy Bound ◽  
Spatial Boundedness

Reconstructions of asymmetric objects computed by electron tomography are distorted due to the absence of information, usually in an angular range from 60 to 90°, which produces a “missing wedge” in Fourier space. These distortions often interfere with the interpretation of results and thus limit biological ultrastructural information which can be obtained. We have attempted to use the Method of Projections Onto Convex Sets (POCS) for restoring the missing information. In POCS, use is made of the fact that known constraints such as positivity, spatial boundedness or an upper energy bound define convex sets in function space. Enforcement of such constraints takes place by iterating a sequence of function-space projections, starting from the original reconstruction, onto the convex sets, until a function in the intersection of all sets is found. First applications of this technique in the field of electron microscopy have been promising.To test POCS on experimental data, we have artificially reduced the range of an existing projection set of a selectively stained Golgi apparatus from ±60° to ±50°, and computed the reconstruction from the reduced set (51 projections). The specimen was prepared from a bull frog spinal ganglion as described by Lindsey and Ellisman and imaged in the high-voltage electron microscope.

Finite-order Integration Weights Can be Dangerous

2007 ◽  
Vol 7 (3) ◽  
pp. 239-254 ◽  
Author(s):  
I.H. Sloan
Keyword(s):  
Function Space ◽  
Finite Order ◽  
Small Subset ◽  
Worst Case ◽  
Integration Rule ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Sum Of Functions ◽  
Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

A Function Space Approach to Spectral Related Problems

2019 ◽  
Vol 10 (6) ◽  
pp. 1220-1222
Author(s):  
T. Venkatesh ◽  
Karuna Samaje
Keyword(s):  
Function Space ◽  
Space Approach
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