Finite heat kernel expansions on the real line
Iliev, Plamen
arXiv, 0504046 / Harvested from arXiv
Text on arXiv
Let L=d^2/dx^2+u(x) be the one-dimensional Schrodinger operator and H(x,y,t) be the corresponding heat kernel. We prove that the nth Hadamard's coefficient H_n(x,y) is equal to 0 if and only if there exists a differential operator M of order 2n-1 such that L^{2n-1}=M^2. Thus, the heat expansion is finite if and only if the potential u(x) is a rational solution of the KdV hierarchy decaying at infinity studied in [1,2]. Equivalently, one can characterize the corresponding operators L as the rank one bispectral family in [8].
Publié le : 2005-04-14
Classification:  Mathematical Physics 
@article{0504046,
     author = {Iliev, Plamen},
     title = {Finite heat kernel expansions on the real line},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504046}
}

Iliev, Plamen. Finite heat kernel expansions on the real line. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504046/