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pro vyhledávání: '"Gibson, Peter C."'
Autor:
Gibson, Peter C.
The classical Szeg\H{o}-Verblunsky theorem relates integrability of the logarithm of the absolutely continuous part of a probability measure on the circle to square summability of the sequence of recurrence coefficients for the orthogonal polynomials
Externí odkaz:
http://arxiv.org/abs/2202.10334
Autor:
Gibson, Peter C.
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular than can b
Externí odkaz:
http://arxiv.org/abs/2108.09799
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the wave speed u
Externí odkaz:
http://arxiv.org/abs/1912.05360
Autor:
Gibson, Peter C.
The one dimensional wave equation serves as a basic model for imaging modalities such as seismic which utilize acoustic data reflected back from a layered medium. In 1955 Peterson et al. described a single scattering approximation for the one dimensi
Externí odkaz:
http://arxiv.org/abs/1703.04162
Autor:
Gibson, Peter C.
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.
Comment: 11 pages, 3 figures
Comment: 11 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/1703.04125
Autor:
Gibson, Peter C.
A family of orthogonal polynomials on the disk (which we call scattering polynomials) serves to formulate a remarkable Fourier expansion of the composition of a sequence of Poincar\'e disk automorphisms. Scattering polynomials are tied to an exotic r
Externí odkaz:
http://arxiv.org/abs/1603.02304
Autor:
Gibson, Peter C.
We introduce a new family of orthogonal polynomials on the disk that has emerged in the context of wave propagation in layered media. Unlike known examples, the polynomials are orthogonal with respect to a measure all of whose even moments are infini
Externí odkaz:
http://arxiv.org/abs/1503.05402
Autor:
GIBSON, PETER C.
Publikováno v:
SIAM Journal on Mathematical Analysis; 2024, Vol. 56 Issue 4, p4466-4493, 28p
Autor:
Gibson, Peter C.
Layered media have been studied extensively both for their importance in imaging technologies and as an example of a hyperbolic PDE with discontinuous coefficients. From the perspective of acoustic imaging, the time limited impulse response at the bo
Externí odkaz:
http://arxiv.org/abs/1412.6138