The Asymptotic Behavior of Singular Numbers of Compact Pseudodifferential Operators with Symbol Nonsmooth in Spatial Variables

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The Asymptotic Behavior of Singular Numbers of Compact Pseudodifferential Operators with Symbol Nonsmooth in Spatial Variables. / Karol’, A. I.

In: Functional Analysis and its Applications, Vol. 53, No. 4, 01.10.2019, p. 313-316.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{e20f1423123b43799a0557ffcc1b214b,

title = "The Asymptotic Behavior of Singular Numbers of Compact Pseudodifferential Operators with Symbol Nonsmooth in Spatial Variables",

abstract = "Compact pseudodifferential operators whose symbol fails to be smooth with respect to x on a given set are considered. Conditions under which Weyl{\textquoteright}s law of spectral asymptotics remains valid for such operators are obtained. The results are applied to operators with symbols such that their order of decay as |ξ| → ∞ is a nonsmooth function of x.",

keywords = "bounds for singular numbers, nonsmooth symbol, pseudodifferential operator, spectral asymptotics",

author = "Karol{\textquoteright}, {A. I.}",

note = "Funding Information: This work was supported by RFBR grant no. 18-01-00472. Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2019",

month = oct,

day = "1",

doi = "10.1134/S0016266319040099",

language = "English",

volume = "53",

pages = "313--316",

journal = "Functional Analysis and its Applications",

issn = "0016-2663",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - The Asymptotic Behavior of Singular Numbers of Compact Pseudodifferential Operators with Symbol Nonsmooth in Spatial Variables

AU - Karol’, A. I.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - Compact pseudodifferential operators whose symbol fails to be smooth with respect to x on a given set are considered. Conditions under which Weyl’s law of spectral asymptotics remains valid for such operators are obtained. The results are applied to operators with symbols such that their order of decay as |ξ| → ∞ is a nonsmooth function of x.

AB - Compact pseudodifferential operators whose symbol fails to be smooth with respect to x on a given set are considered. Conditions under which Weyl’s law of spectral asymptotics remains valid for such operators are obtained. The results are applied to operators with symbols such that their order of decay as |ξ| → ∞ is a nonsmooth function of x.

KW - bounds for singular numbers

KW - nonsmooth symbol

KW - pseudodifferential operator

KW - spectral asymptotics

UR - http://www.scopus.com/inward/record.url?scp=85078334877&partnerID=8YFLogxK

U2 - 10.1134/S0016266319040099

DO - 10.1134/S0016266319040099

M3 - Article

AN - SCOPUS:85078334877

VL - 53

SP - 313

EP - 316

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 4

ER -

ID: 71278112