JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A CHANGE OF SCALE FORMULA FOR WIENER INTEGRALS OF UNBOUNDED FUNCTIONS II
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A CHANGE OF SCALE FORMULA FOR WIENER INTEGRALS OF UNBOUNDED FUNCTIONS II
Yoo, Il; Song, Teuk-Seob; Kim, Byoung-Soo;
  PDF(new window)
 Abstract
Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S of analytic Feynman integrable functions on classical Wiener space. Yoo and Skoug extended these results to abstract Wiener space for a generalized Fresnel class containing the Fresnel class F(B) which corresponds to the Banach algebra S on classical Wiener space. In this paper, we present a change of scale formula for Wiener integrals of various functions on which need not be bounded or continuous.
 Keywords
Wiener integral;Feynman integral;change of scale formula;Fresnel class;
 Language
English
 Cited by
1.
GENERALIZED ANALYTIC FEYNMAN INTEGRAL VIA FUNCTION SPACE INTEGRAL OF BOUNDED CYLINDER FUNCTIONALS,;;;

대한수학회보, 2011. vol.48. 3, pp.475-489 crossref(new window)
2.
RELATIONSHIP BETWEEN THE WIENER INTEGRAL AND THE ANALYTIC FEYNMAN INTEGRAL OF CYLINDER FUNCTION,;

충청수학회지, 2014. vol.27. 2, pp.249-260 crossref(new window)
3.
CHANGE OF SCALE FORMULAS FOR FUNCTION SPACE INTEGRALS RELATED WITH FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION ON Ca,b[0, T],;;;

Korean Journal of Mathematics, 2015. vol.23. 1, pp.47-64 crossref(new window)
1.
Fourier-Feynman transforms of unbounded functionals on abstract Wiener space, Central European Journal of Mathematics, 2010, 8, 3, 616  crossref(new windwow)
2.
Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and Convolution, Journal of Function Spaces, 2014, 2014, 1  crossref(new windwow)
3.
CHANGE OF SCALE FORMULAS FOR FUNCTION SPACE INTEGRALS RELATED WITH FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION ON Ca,b[0, T], Korean Journal of Mathematics, 2015, 23, 1, 47  crossref(new windwow)
4.
RELATIONSHIP BETWEEN THE WIENER INTEGRAL AND THE ANALYTIC FEYNMAN INTEGRAL OF CYLINDER FUNCTION, Journal of the Chungcheong Mathematical Society, 2014, 27, 2, 249  crossref(new windwow)
5.
GENERALIZED ANALYTIC FEYNMAN INTEGRAL VIA FUNCTION SPACE INTEGRAL OF BOUNDED CYLINDER FUNCTIONALS, Bulletin of the Korean Mathematical Society, 2011, 48, 3, 475  crossref(new windwow)
6.
Integration by parts formulas for analytic Feynman integrals of unbounded functionals, Integral Transforms and Special Functions, 2009, 20, 1, 45  crossref(new windwow)
 References
1.
J. M. Ahn, G. W. Johnson and D. L. Skoug, Functions in the Fresnel Class of an Abstract Wiener Space, J. Korean Math. Soc. 28 (1991), no. 2, 245-265

2.
R. H. Cameron, The Translation Pathology of Wiener Space, Duke Math. J. 21 (1954), 623-628 crossref(new window)

3.
R. H. Cameron and W. T. Martin, The Behavior of Measure and Measurability under Change of Scale in Wiener Space, Bull. Amer. Math. Soc. 53 (1947), 130-137 crossref(new window)

4.
R. H. Cameron and D. A. Storvick, Some Banach Algebras of Analytic Feynman Integrable functionals, in Analytic Functions, Kozubnik, Lecture Notes in Math. 798 (1980), 18-27 crossref(new window)

5.
R. H. Cameron and D. A. Storvick, Change of Scale Formulas for Wiener Integral, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero 17 (1987), 105-115

6.
R. H. Cameron and D. A. Storvick, Relationships between the Wiener Integral and the Analytic Feynman Integral, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero 17 (1987), 117-133

7.
R. H. Cameron and D. A. Storvick, New Existence Theorems and Evaluation Formulas for Analytic Feynman Integrals, Deformations of Mathematics Structures, 297-308, Kluwer, Dordrecht, 1989

8.
K. S. Chang, Scale-Invariant Measurability in Yeh-Wiener Space, J. Korean Math. Soc. 21 (1982), no. 1, 61-67

9.
K. S. Chang, G. W. Johnson and D. L. Skoug, Necessary and Sufficient Con- ditions for the Fresnel Integrability of Certain Classes of Functions, J. Korean Math. Soc. 21 (1984), no. 1, 21-29

10.
K. S. Chang, G. W. Johnson and D. L. Skoug, Functions in the Fresnel Class, Proc. Amer. Math. Soc. 100 (1987), 309-318 crossref(new window)

11.
K. S. Chang, G. W. Johnson and D. L. Skoug, Necessary and Sufficient Conditions for Membership in the Banach Algebra S for Certain Classes of Functions, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero 17 (1987), 153-171

12.
K. S. Chang, G. W. Johnson and D. L. Skoug, Functions in the Banach Algebra S(v), J. Korean Math. Soc. 24 (1987), no. 2, 151-158

13.
K. S. Chang, B. S. Kim and I. Yoo, Analytic Fourier-Feynman Transform and Convolution of Functionals on Abstract Wiener Space, Rocky Mountain J. Math. 30 (2000), 823-842 crossref(new window)

14.
D. M. Chung, Scale-Invariant Measurability in Abstract Wiener Space, Paciffic J. Math. 130 (1987), 27-40 crossref(new window)

15.
L. Gross, Abstract Wiener Space, Proc. 5th Berkeley Sympos. Math. Stat. Prob. 2 (1965), 31-42

16.
G. W. Johnson and D. L. Skoug, Scale-Invariant Measurability in Wiener Space, Paciffic J. Math. 83 (1979), 157-176 crossref(new window)

17.
G. W. Johnson and D. L. Skoug, Stability Theorems for the Feynman Integral, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero 8 (1985), 361-367

18.
G. Kallianpur and C. Bromley, Generalized Feynman Integrals using Analytic Continuation in Several Complex Variables, in Stochastic Analysis and Applica- tions (ed. M.H. Pinsky), 433-450, Dekker, New York, 1984

19.
G. Kallianpur, D. Kannan and R. L. Karandikar, Analytic and Sequential Feyn- man Integrals on Abstract Wiener and Hilbert Spaces and a Cameron-Martin Formula, Ann. Inst. Henri Poincare, 21 (1985), 323-361

20.
H. H. Kuo, Gaussian Measures in Banach Spaces, Springer Lecture Notes in Math. 463 (1975), Berlin-New York

21.
I. Yoo and K. S. Chang, Notes on Analytic Feynman Integrable Functions, Rocky Mountain J. Math. 23 (1993), 1133-1142 crossref(new window)

22.
I. Yoo and D. L. Skoug, A Change of Scale Formula for Wiener Integrals on Abstract Wiener Spaces, Internat. J. Math. Math. Sci. 17 (1994), 239-248 crossref(new window)

23.
I. Yoo and D. L. Skoug, A Change of Scale Formula for Wiener Integrals on Abstract Wiener Spaces II, J. Korean Math. Soc. 31 (1994), 115-129

24.
I. Yoo, T. S. Song, B. S. Kim and K. S. Chang, A Change of Scale Formula for Wiener Integrals of Unbounded Functions, Rocky Mountain J. Math. 34 (2004), 371-389 crossref(new window)

25.
I. Yoo and G. J. Yoon, Change of Scale Formulas for Yeh-Wiener Integrals, Commun. Korean Math. Soc. 6 (1991), no. 1, 19-26