Finite heat kernel expansions on the real line
نویسندگان
چکیده
منابع مشابه
Finite Heat Kernel Expansions on the Real Line
Let L = d/dx +u(x) be the one-dimensional Schrödinger operator and H(x, y, t) be the corresponding heat kernel. We prove that the nth Hadamard’s coefficient Hn(x, y) is equal to 0 if and only if there exists a differential operator M of order 2n− 1 such that L = M. Thus, the heat expansion is finite if and only if the potential u(x) is a rational solution of the KdV hierarchy decaying at infini...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-07-08677-7