A Banach algebra with its applications over paths of bounded variation

@article{Cho2018ABA,
  title={A Banach algebra with its applications over paths of bounded variation},
  author={Dong Hyun Cho},
  journal={Advances in Operator Theory},
  year={2018}
}
  • D. Cho
  • Published 1 September 2018
  • Mathematics
  • Advances in Operator Theory
Let C[0, T ] denote the space of continuous real-valued functions on [0, T ]. In this paper we introduce two Banach algebras: one of them is defined on C[0, T ] and the other is a space of equivalence classes of measures over paths of bounded variation on [0, T ]. We establish an isometric isomorphism between them and evaluate analytic Feynman integrals of the functions in the Banach algebras, which play significant roles in the Feynman integration theories and quantum mechanics. 
View via Publisher
aot-math.org
1 Citations

One Citation

A Banach algebra of series of functions over paths

Let $C[0,T]$ denote the space of continuous real-valued functions on $[0,T]$. On the space $C[0,T]$, we introduce a Banach algebra of series of functions which are generalized Fourier-Stieltjes…

References

SHOWING 1-7 OF 7 REFERENCES

THE TRANSLATION THEOREM ON THE GENERALIZED ANALOGUE OF WIENER SPACE AND ITS APPLICATIONS

In this note, we prove the translation theorem for the generalized analogue of Wiener measure space and we show some properties of the generalized analogue of Wiener measure from it. 1. Preliminaries…

On a Family of Generalized Wiener Spaces and Applications

We investigate the structure and properties of a variety of generalized Wiener spaces. Our main focus is on Wiener-type measures on spaces of continuous functions; our generalizations include an…

Space-Time Approach to Non-Relativistic Quantum Mechanics

Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which…

and s

THE GENERALIZED ANALOGUE OF WIENER MEASURE SPACE AND ITS PROPERTIES

In this note, we introduce the deflnition of the gener- alized analogue of Wiener measure on the space C(a;b) of all real- valued continuous functions on the closed interval (a;b), give several…

Some banach algebras of analytic feynman integrable functionals

Generalized Feynman integrals using analytic continuation in several complex variables, Stochastic analysis and applications, 217–267, Adv

  • Probab. Related Topics, 7, Dekker, New York,
  • 1984