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An abstract approach to pointwise decay estimates for dispersive equations
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Larenas, Manuel. An abstract approach to pointwise decay estimates for dispersive equations. Retrieved from https://doi.org/doi:10.7282/T3D220KW

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TitleAn abstract approach to pointwise decay estimates for dispersive equations
NameLarenas, Manuel (author); Soffer, Avy (chair); Kiessling, Michael (internal member); Tahvildar-Zadeh, Shadi (internal member); Georgescu, Vladimir (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2015
Other Date2015-10 (degree)
SubjectMathematics
Extent1 online resource (vi, 62 p. : ill.)
DescriptionIn the study of dispersive equations one is faced with the need to quantitatively estimate the decay rate of the solution in various norms. The pointwise decay estimates are particularly useful in applications, for instance, to prove asymptotic stability of solutions or to obtain the more general Lp decay estimates. In this dissertation we develop a new abstract theory to prove pointwise decay estimates in weighted spaces, starting only from a general commutator identity that should be satisfied by the Hamiltonian H and a conjugate operator A. We show that for Schrodinger type equations generated by an abstract H, the identity [H,iA] = g (H)+K combined with Kato-smoothness of K and a regularity assumption of the type H in C^1(A), are sufficient to prove pointwise decay estimates of the Kato-Jensen type. Our results apply at energy thresholds and do not explicitly use the kernel of the (unperturbed) Hamiltonian. Consequently, they are easier to implement on manifolds. We give several examples to show that such pointwise estimates follow effortlessly from the general theory.
NotePh.D.
NoteIncludes bibliographical references
Noteby Manuel Larenas
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3D220KW
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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