Operator-Valued Pseudodifferential Operators and the Resolvent of a Degenerate Elliptic Operator

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Operator-Valued Pseudodifferential Operators and the Resolvent of a Degenerate Elliptic Operator. / Karol, A. I.; Seeley, R.

In: Mathematics of the USSR - Sbornik, Vol. 49, No. 2, 28.02.1984, p. 553-567.

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

BibTeX

@article{8977a11f15ad4800bf47ed90c52b2490,

title = "Operator-Valued Pseudodifferential Operators and the Resolvent of a Degenerate Elliptic Operator",

abstract = "In this paper the author constructs an asymptotic expansion of the resolvent of the operator of the Dirichlet problem for an elliptic equation of divergence form with a power degeneracy on the boundary. To construct the expansion a variant of the technique of pseudodifferential operators (DO{\textquoteright}s) with operator-valued symbols is used, in combination with the technique of “ordinary” scalar iDO{\textquoteright}s. The difference between the resolvent and the approximation thus obtained is an integral operator whose kernel decreases at infinity faster than any power of the spectral parameter. In a neighborhood of the boundary this operator smooths only in directions tangent to the boundary.",

author = "Karol, {A. I.} and R. Seeley",

year = "1984",

month = feb,

day = "28",

doi = "10.1070/SM1984v049n02ABEH002727",

language = "English",

volume = "49",

pages = "553--567",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "2",

}

RIS

TY - JOUR

T1 - Operator-Valued Pseudodifferential Operators and the Resolvent of a Degenerate Elliptic Operator

AU - Karol, A. I.

AU - Seeley, R.

PY - 1984/2/28

Y1 - 1984/2/28

N2 - In this paper the author constructs an asymptotic expansion of the resolvent of the operator of the Dirichlet problem for an elliptic equation of divergence form with a power degeneracy on the boundary. To construct the expansion a variant of the technique of pseudodifferential operators (DO’s) with operator-valued symbols is used, in combination with the technique of “ordinary” scalar iDO’s. The difference between the resolvent and the approximation thus obtained is an integral operator whose kernel decreases at infinity faster than any power of the spectral parameter. In a neighborhood of the boundary this operator smooths only in directions tangent to the boundary.

AB - In this paper the author constructs an asymptotic expansion of the resolvent of the operator of the Dirichlet problem for an elliptic equation of divergence form with a power degeneracy on the boundary. To construct the expansion a variant of the technique of pseudodifferential operators (DO’s) with operator-valued symbols is used, in combination with the technique of “ordinary” scalar iDO’s. The difference between the resolvent and the approximation thus obtained is an integral operator whose kernel decreases at infinity faster than any power of the spectral parameter. In a neighborhood of the boundary this operator smooths only in directions tangent to the boundary.

UR - http://www.scopus.com/inward/record.url?scp=84956276078&partnerID=8YFLogxK

U2 - 10.1070/SM1984v049n02ABEH002727

DO - 10.1070/SM1984v049n02ABEH002727

M3 - Article

AN - SCOPUS:84956276078

VL - 49

SP - 553

EP - 567

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 2

ER -

ID: 71278356