The Index of the Complex Eigenvalues of a Parity Progressive Population Operator[J] . Xue-Zhi Li,Geni Gupur,Yong-Jiang Yu,Guang-Tian Zhu.Journal of Mathematical Analysis and Applications . 2002 (2)Li Xue-Zhi.The Index of the Complex Eigenvalues of a Parity Progressive Population Operator[J]....
Finally, to control we see from (4) and (8) that has an operator norm of at most . In particular, we have from the Cauchy-Schwarz inequality that for any . Let be the set of all pairs where either , , , or One easily verifies that (2) holds. If is not in , then by ...
Of particular interest for us is the following result about the absence of real eigenvalues in , equivalently about the distribution function of the largest real eigenvalue in the finite n GinOE. Proposition 1.1 ([56, Proposition 2.2]) For every , (1.1) where is the operator of ...
2 [9]. In the case of a spherically symmetric potential this is still true for the Dirac operator restricted to a subspace of definite angular momentum and definite parity (radial Dirac operator) [9]. We rederive this result for the radial Dirac operator by a new method......
The calculation of upper and lower bounds for the Schr枚dinger-equation eigenvalues from moment recurrence relations is reviewed. A previous algorithm originally developed to approach the ground state is shown to apply also to the first excited state of parity-invariant systems. Alternative recurrence ...