Asymptotic shape of solutions to nonlinear eigenvalue problems.
Shibata, Tetsutaro (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Shibata, Tetsutaro (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Lu, Chunqing (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Djalil Kateb, Pierre Gilles Lemarié-Rieusset (1997)
Revista Matemática Iberoamericana
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We give the first term of the asymptotic development for the phase of the N-th (minimum-phased) Daubechies filter as N goes to +∞. We obtain this result through the description of the complex zeros of the associated polynomial of degree 2N+1.
D. Przeworska-Rolewicz (1969)
Studia Mathematica
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A. Bazylewicz (1976)
Acta Arithmetica
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K. Ramanathan (1984)
Acta Arithmetica
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Liang-Cheng Zhang (1997)
Acta Arithmetica
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Ryuichi Ishimura, Yasunori Okada (1994)
Bulletin de la Société Mathématique de France
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Mahta Khosravi, John A. Toth (2005)
Annales de l'institut Fourier
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Let be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that , where is a specific nonzero constant and is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the -dimensional case. ...