Abstract
We find that, in the critical case \(2l= {\mathbf N} \), the eigenvalues of the problem \(\lambda(-\Delta)^{l}u=Pu\) with the singular measure \(P\) supported on a compact Lipschitz surface of an arbitrary dimension in \( {\mathbb R} ^{ {\mathbf N} }\) satisfy an asymptotic formula of the same order as in the case of an absolutely continuous measure.
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 113–117 https://doi.org/10.4213/faa3856.
To the memory of M. Z. Solomyak, a great mathematician and an extraordinary person
Translated by G. V. Rozenblum
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Rozenblum, G.V., Shargorodsky, E.M. Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case. Funct Anal Its Appl 55, 170–173 (2021). https://doi.org/10.1134/S001626632102009X
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DOI: https://doi.org/10.1134/S001626632102009X