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The various definitions of the derivative in linear topological spaces
The object of this article is to give a survey of the existing definitions of the operation of differentiation in linear topological spaces (l.t.s.) and to show the connections between them. ThereExpand
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Analytic properties of infinite-dimensional distributions
CONTENTS Introduction ??1. Notations, terminology, and auxiliary results ??2. The analytic properties of measures ??3. The properties of subspaces of differentiability ??4. The smoothness of someExpand
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The theory of differentiation in linear topological spaces
CONTENTSIntroductionChapter I. Differentiation along a subspace § 1. Definition of the first derivative § 2. Formal rules of differentiation § 3. The mean value theorem. Partial derivatives § 4.Expand
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This survey contains some results on measures in linear topological spaces and in completely regular topological spaces. These results are important in the theory of linear differential equationsExpand
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Hamilton-Jacobi-Bellman equations for quantum optimal feedback control
We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We deriveExpand
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Noether’s theorem for dissipative quantum dynamical semi-groups
Noether’s theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong [J. Math. Phys. 54, 013301Expand
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Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds
Let $(S(t))_{t \ge 0}$ be a one-parameter family of positive integral operators on a locally compact space $L$. For a possibly non-uniform partition of $[0,1]$ define a finite measure on the pathExpand
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Hamiltonian Feynman path integrals via the Chernoff formula
The main aim of the present paper is using a Chernoff theorem (i.e., the Chernoff formula) to formulate and to prove some rigorous results on representations for solutions of Schrodinger equations byExpand
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Ordinary differential equations in locally convex spaces
CONTENTS Introduction §1. Equations with continuous right-hand side 1.1. Some definitions and notation 1.2. Peano's theorem 1.3. Kneser's theorem 1.4. Continuous dependence on initial data 1.5. JointExpand
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