Derivative of the Donsker delta functionals

Herry Pribawanto Suryawan

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 2, page 161-176
  • ISSN: 0862-7959

Abstract

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We prove that derivatives of any finite order of Donsker's delta functionals are well-defined elements in the space of Hida distributions. We also show the convergence to the derivative of Donsker's delta functionals of two different approximations. Finally, we present an existence result of finite product and infinite series of the derivative of the Donsker delta functionals.

How to cite

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Suryawan, Herry Pribawanto. "Derivative of the Donsker delta functionals." Mathematica Bohemica 144.2 (2019): 161-176. <http://eudml.org/doc/294432>.

@article{Suryawan2019,
abstract = {We prove that derivatives of any finite order of Donsker's delta functionals are well-defined elements in the space of Hida distributions. We also show the convergence to the derivative of Donsker's delta functionals of two different approximations. Finally, we present an existence result of finite product and infinite series of the derivative of the Donsker delta functionals.},
author = {Suryawan, Herry Pribawanto},
journal = {Mathematica Bohemica},
keywords = {Donsker delta functional; white noise analysis; distributional derivative},
language = {eng},
number = {2},
pages = {161-176},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derivative of the Donsker delta functionals},
url = {http://eudml.org/doc/294432},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Suryawan, Herry Pribawanto
TI - Derivative of the Donsker delta functionals
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 2
SP - 161
EP - 176
AB - We prove that derivatives of any finite order of Donsker's delta functionals are well-defined elements in the space of Hida distributions. We also show the convergence to the derivative of Donsker's delta functionals of two different approximations. Finally, we present an existence result of finite product and infinite series of the derivative of the Donsker delta functionals.
LA - eng
KW - Donsker delta functional; white noise analysis; distributional derivative
UR - http://eudml.org/doc/294432
ER -

References

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