On Volterra integral operators with highly oscillatory kernels | Zendy

Hermann Brunner | Zendy

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On Volterra integral operators with highly oscillatory kernels

Author(s) -

Hermann Brunner

Publication year - 2013

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2014.34.915

Subject(s) - volterra integral equation , uncountable set , integral equation , oscillation (cell signaling) , mathematics , volterra equations , fourier integral operator , singular integral , daniell integral , focus (optics) , mathematical analysis , pure mathematics , nonlinear system , physics , quantum mechanics , countable set , biology , optics , genetics

We study the high-oscillation properties of solutions to integral equations associated with two classes of Volterra integral operators: compact operators with highly oscillatory kernels that are either smooth or weakly singular, and noncompact cordial Volterra integral operators with highly oscillatory kernels. In the latter case the focus is on the dependence of the (uncountable) spectrum on the oscillation parameter. It is shown that the results derived in this paper merely open a window to a general theory of solutions of highly oscillatory Volterra integral equations, and many questions remain to be answered

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