Functions of four variables which satisfy both the heat equation and the Laplace equation in three variables - II

Gupta, P.M.; Kulshreshtha, S.K.

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The solution of the two-point boundary value problem for a nonlinear differential equation of the third order

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The mean square of the error term in a generalization of Dirichlet's divisor problem

Tom Meurman (1996)

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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.

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Shibata, Tetsutaro (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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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 $\int_{1}^{T} {| R (t) |}^{2} d t = c T^{\frac{5}{2}} + O_{δ} (T^{\frac{9}{4} + δ})$ , 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 $R (t) = O_{δ} (t^{\frac{3}{4} + δ})$ .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. ...

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

On Meijer transform

The solution of the two-point boundary value problem for a nonlinear differential equation of the third order

The mean square of the error term in a generalization of Dirichlet's divisor problem

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

Precise asymptotic behavior of solutions to damped simple pendulum equations.

The phase of the Daubechies filters.

Cramér's formula for Heisenberg manifolds

Short-time heat flow and functions of bounded variation in $R^{N}$