Abstract
In this paper, we study the geometry associated with Schrödinger operator via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique, we construct the heat kernel with the coefficient matrices of the operator both diagonal and non-diagonal. For applications, we compute the heat kernel of a Schrödinger operator with terms of lower order, and obtain a globally closed solution to a matrix Riccati equations as a by-product. Besides, we finally recover and generalise several classical results on some celebrated operators.
Citation
Sheng-Ya Feng. "FUNDAMENTAL SOLUTIONS ON PARTIAL DIFFERENTIAL OPERATORS OF SECOND ORDER WITH APPLICATION TO MATRIX RICCATI EQUATIONS." Taiwanese J. Math. 17 (2) 379 - 406, 2013. https://doi.org/10.11650/tjm.17.2013.2108
Information