Estimates of the Spectrum in the Interval

Victor Ivrii ()
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Victor Ivrii: University of Toronto, Department of Mathematics

Chapter Chapter 10 in Microlocal Analysis, Sharp Spectral Asymptotics and Applications II, 2019, pp 45-93 from Springer

Abstract: Abstract Here $$E(A;\tau _1,\tau _2)$$ is the spectral projector corresponding to the open interval $$(\tau _1,\tau _2)$$ rather than to more standard semi-open interval $$[\tau _1,\tau _2)$$ as before and $${\mathsf {N}}(A;\tau _1,\tau _2)$$ is number of eigenvalues in $$(\tau _1,\tau _2)$$ counting their multiplicities, unless $$(\tau _1,\tau _2)\cap {\text {Spec}}_{{\mathsf {ess}}}(A)\ne \emptyset $$ in which case $${\mathsf {N}}(A;\tau _1,\tau _2)=\infty $$ .

Date: 2019
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DOI: 10.1007/978-3-030-30541-3_10

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