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This book is an outgrowth of ideas originating from 1. Kluvanek.
Unfortunately, Professor Kluvanek did not live to contribute to the
project of writing up in a systematic form, the circle of ideas to
which the present work is devoted. It is more than likely that with
his input, the approach and areas of emphasis of the resulting
exposition would have been quite different from what we have here.
Nevertheless, the stamp of Kluvanek's thought and philosophy (but
not necessarily his approval) abounds throughout this book.
Although the title gives no indication, integration theory in
vector spaces is a cen tral topic of this work. However, the
various notions of integration developed here are intimately
connected with a specific application-the representation of
evolutions by func tional integrals. The representation of a
perturbation to the heat semigroup in terms of Wiener measure is
known as the Feynman-Kac formula, but the term has a wider meaning
in the present work. Traditionally, such representations have been
used to obtain analytic information about perturbations to free
evolutions as an alternative to arguments with a more
operator-theoretic flavour. No applications of this type are given
here. It is an un derlying assumption of the presentation of this
material that representations of the nature of the Feynman-Kac
formula are worth obtaining, and in the process of obtaining them,
we may be led to new, possibly fertile mathematical structures-a
view largely motivated by the pervasive use of path integrals in
quantum physics."
This book is an outgrowth of ideas originating from 1. Kluvanek.
Unfortunately, Professor Kluvanek did not live to contribute to the
project of writing up in a systematic form, the circle of ideas to
which the present work is devoted. It is more than likely that with
his input, the approach and areas of emphasis of the resulting
exposition would have been quite different from what we have here.
Nevertheless, the stamp of Kluvanek's thought and philosophy (but
not necessarily his approval) abounds throughout this book.
Although the title gives no indication, integration theory in
vector spaces is a cen tral topic of this work. However, the
various notions of integration developed here are intimately
connected with a specific application-the representation of
evolutions by func tional integrals. The representation of a
perturbation to the heat semigroup in terms of Wiener measure is
known as the Feynman-Kac formula, but the term has a wider meaning
in the present work. Traditionally, such representations have been
used to obtain analytic information about perturbations to free
evolutions as an alternative to arguments with a more
operator-theoretic flavour. No applications of this type are given
here. It is an un derlying assumption of the presentation of this
material that representations of the nature of the Feynman-Kac
formula are worth obtaining, and in the process of obtaining them,
we may be led to new, possibly fertile mathematical structures-a
view largely motivated by the pervasive use of path integrals in
quantum physics."
Devon Walker had a normal life until an unfortunate run-in with
local delinquent and gang member Roland Chambers led him down a
path of violence and obsessive hatred. When he is pushed past his
limits he is forced to fight back, and with a gang of his own.
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