Several Formulas for the First Regularized Trace of Discrete Operators |
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Authors: | Tomin N G |
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Institution: | (1) Ivanovo State Textile Academy, Russia |
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Abstract: | We derive several abstract formulas (of Gelfand--Levitan type) for the first regularized trace of discrete operators under various conditions convenient for verification. The proof of the main result is based on the contour integration method with some modifications from analytic perturbation theory and from the approach proposed earlier by M. Dostani . Some known trace formulas are generalized and improved. We give examples of the applications of our abstract trace formulas for obtaining special trace formulas for ordinary differential operators and for partial differential operators. |
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Keywords: | regularized trace discrete operator abstract Gelfand--Levitan formula contour integration Sturm-Liouville problem Dirichlet problem Neumann problem |
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