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J. Korean Math. Soc. 2002; 39(4): 559-577
Printed July 1, 2002
Copyright © The Korean Mathematical Society.
New results on stability properties for the Feynman integral via additive functionals
Jung-Ah Lim
University of Nebraska-Lincoln
It is known that the analytic operator-valued Feynman integral exists for some ``potentials'' which are so singular that they must be given by measures rather than by functions. Corresponding stability results involving monotonicity assumptions have been established by the author and others. Here in our main theorem we prove further stability theorem without monotonicity requirements.
Keywords: analytic Feynman integral, stability theorem, generalized Kato class measure, smooth measure, perturbation theorem, closed form, self-adjoint operator
MSC numbers: Primary 28C20; Secondary 28A33, 47D45
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