Displaying similar documents to “Functions of four variables which satisfy both the heat equation and the Laplace equation in three variables - II”

Short-time heat flow and functions of bounded variation in R N

Michele Miranda, Diego Pallara, Fabio Paronetto, Marc Preunkert (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove a characterisation of sets with finite perimeter and B V functions in terms of the short time behaviour of the heat semigroup in R N . For sets with smooth boundary a more precise result is shown.

The phase of the Daubechies filters.

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.

Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

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Let R ( λ ) be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that ∫ 1 T | R ( t ) | 2 d t = c T 5 2 + O δ ( T 9 4 + δ ) , where c is a specific nonzero constant and δ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that R ( t ) = O δ ( t 3 4 + δ ) .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 2 n + 1 -dimensional case. ...