• Publications
  • Influence
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
  • 111
  • 6
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
  • 86
  • 5
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
  • 126
  • 4
MEASURES ON LINEAR TOPOLOGICAL SPACES
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
  • 59
  • 3
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
  • 40
  • 2
  • PDF
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
  • 12
  • 2
  • PDF
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
  • 86
  • 1
  • PDF
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
  • 97
  • 1
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
  • 30
  • 1