A Banach algebra of Feynman integrable functionals with application to an integral equation formally equivalent to Schroedinger's equation |
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Authors: | GW Johnson DL Skoug |
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Institution: | Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68508 USA |
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Abstract: | A Banach algebra A of functionals on Ca, b] is introduced and it is proved that the operator-valued Feynman integral recently defined by Cameron and Storvick exists for functionals in A. Two existence theorems of Cameron and Storvick are seen to be special cases of this result; in fact, even in these cases, the present theorem gives improved results.Cameron and Storvick have used their function space integral to give a solution to an integral equation formally equivalent to Schroedinger's equation; using our existence theorem, we give a relatively brief and transparent proof of this result. |
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