An uncertainty principle related to the Poisson summation formula

K. Gröchenig

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Ewa Damek, Andrzej Hulanicki (2000)

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Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone

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Sigrid Sjöstrand (1970)

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The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin

Paweł Głowacki (1998)

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Let A be a pseudodifferential operator on $ℝ^{N}$ whose Weyl symbol a is a strictly positive smooth function on $W = ℝ^{N} \times ℝ^{N}$ such that $| \partial^{α} a | \leq C_{α} a^{1 - ϱ}$ for some ϱ>0 and all |α|>0, $\partial^{α} a$ is bounded for large |α|, and $l i m_{w \to \infty} a (w) = \infty$ . Such an operator A is essentially selfadjoint, bounded from below, and its spectrum is discrete. The remainder term in the Weyl asymptotic formula for the distribution of the eigenvalues of A is estimated. This is done by applying the method of approximate spectral projectors of Tulovskiĭ and Shubin. ...

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G. Folland (1979)

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