Volume 25, Issue 1
Eigenvalue Problem of Doubly Stochastic Hamiltonian Systems with Boundary Conditions

Yuecai Han & Yong Ma

Commun. Math. Res., 25 (2009), pp. 30-36.

Published online: 2021-06

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  • Abstract

In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic differential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly.

  • Keywords

doubly stochastic Hamiltonian system, eigenvalue problem, spectrum theory.

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@Article{CMR-25-30, author = {Han , Yuecai and Ma , Yong}, title = {Eigenvalue Problem of Doubly Stochastic Hamiltonian Systems with Boundary Conditions}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {1}, pages = {30--36}, abstract = {

In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic differential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19285.html} }
TY - JOUR T1 - Eigenvalue Problem of Doubly Stochastic Hamiltonian Systems with Boundary Conditions AU - Han , Yuecai AU - Ma , Yong JO - Communications in Mathematical Research VL - 1 SP - 30 EP - 36 PY - 2021 DA - 2021/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19285.html KW - doubly stochastic Hamiltonian system, eigenvalue problem, spectrum theory. AB -

In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic differential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly.

Yuecai Han & YongMa. (2021). Eigenvalue Problem of Doubly Stochastic Hamiltonian Systems with Boundary Conditions. Communications in Mathematical Research . 25 (1). 30-36. doi:
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