A fundamental solution of the parabolic equation on hilbert space. Ii: The semigroup property

M. Ann Piech

doi:10.1090/S0002-9947-1970-0278116-8

A fundamental solution of the parabolic equation on hilbert space. Ii: The semigroup property

M. Ann Piech

Mathematics

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15 Scopus citations

Abstract

The existence of a family of solution operators {q_t: T > 0} corresponding to a fundamental solution of a second order infinite-dimensional differential equation of the form ¶_u/¶_t=Lu was previously established by the author. In the present paper, it is established that these operators are nonnegative, and satisfy the condition q_sq_t=q_s+_t.

Original language	English
Pages (from-to)	257-286
Number of pages	30
Journal	Transactions of the American Mathematical Society
Volume	150
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1970-0278116-8
State	Published - Jul 1970

Keywords

Abstract Wiener space
Fundamental solution
Hilbert space
Parabolic equation
Semigroups of operators
Wiener measure

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10.1090/S0002-9947-1970-0278116-8

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abstract = "The existence of a family of solution operators \{qt: T > 0\} corresponding to a fundamental solution of a second order infinite-dimensional differential equation of the form ¶u/¶t=Lu was previously established by the author. In the present paper, it is established that these operators are nonnegative, and satisfy the condition qsqt=qs+t.",

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AB - The existence of a family of solution operators {qt: T > 0} corresponding to a fundamental solution of a second order infinite-dimensional differential equation of the form ¶u/¶t=Lu was previously established by the author. In the present paper, it is established that these operators are nonnegative, and satisfy the condition qsqt=qs+t.

KW - Abstract Wiener space

KW - Fundamental solution

KW - Hilbert space

KW - Parabolic equation

KW - Semigroups of operators

KW - Wiener measure

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 1

ER -

A fundamental solution of the parabolic equation on hilbert space. Ii: The semigroup property

Abstract

Keywords

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