Dixmier's trace for boundary value problems

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Dixmier's trace for boundary value problems. / Nest, Ryszard; Schrohe, Elmar.

I: Manuscripta Mathematica, Bind 96, Nr. 2, 06.1998, s. 203-218.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Nest, R & Schrohe, E 1998, 'Dixmier's trace for boundary value problems', Manuscripta Mathematica, bind 96, nr. 2, s. 203-218. https://doi.org/10.1007/s002290050062

APA

Nest, R., & Schrohe, E. (1998). Dixmier's trace for boundary value problems. Manuscripta Mathematica, 96(2), 203-218. https://doi.org/10.1007/s002290050062

Vancouver

Nest R, Schrohe E. Dixmier's trace for boundary value problems. Manuscripta Mathematica. 1998 jun.;96(2):203-218. https://doi.org/10.1007/s002290050062

Author

Nest, Ryszard ; Schrohe, Elmar. / Dixmier's trace for boundary value problems. I: Manuscripta Mathematica. 1998 ; Bind 96, Nr. 2. s. 203-218.

Bibtex

@article{d333b832f68744b799d87a533eaf20d7,
title = "Dixmier's trace for boundary value problems",
abstract = "Let X be a smooth manifold with boundary of dimension n > 1. The operators of order -n and type zero in Boutet de Monvel's calculus form a subset of Dixmier's trace ideal ℒ1,∞(H) for the Hilbert space H = L2(X, E) ⊕ L2(∂X, F) of L2 sections in vector bundles E over X, F over ∂X. We show that, on these operators, Dixmier's trace can be computed in terms of the same expressions that determine the noncommutative residue. In particular it is independent of the averaging procedure. However, the noncommutative residue and Dixmier's trace are not multiples of each other unless the boundary is empty. As a corollary we show how to compute Dixmier's trace for parametrices or inverses of classical elliptic boundary value problems of the form Pu = f; Tu = 0 with an elliptic differential operator P of order n in the interior and a trace operator T. In this particular situation, Dixmier's trace and the noncommutative residue do coincide up to a factor.",
author = "Ryszard Nest and Elmar Schrohe",
year = "1998",
month = jun,
doi = "10.1007/s002290050062",
language = "English",
volume = "96",
pages = "203--218",
journal = "Manuscripta Mathematica",
issn = "0025-2611",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Dixmier's trace for boundary value problems

AU - Nest, Ryszard

AU - Schrohe, Elmar

PY - 1998/6

Y1 - 1998/6

N2 - Let X be a smooth manifold with boundary of dimension n > 1. The operators of order -n and type zero in Boutet de Monvel's calculus form a subset of Dixmier's trace ideal ℒ1,∞(H) for the Hilbert space H = L2(X, E) ⊕ L2(∂X, F) of L2 sections in vector bundles E over X, F over ∂X. We show that, on these operators, Dixmier's trace can be computed in terms of the same expressions that determine the noncommutative residue. In particular it is independent of the averaging procedure. However, the noncommutative residue and Dixmier's trace are not multiples of each other unless the boundary is empty. As a corollary we show how to compute Dixmier's trace for parametrices or inverses of classical elliptic boundary value problems of the form Pu = f; Tu = 0 with an elliptic differential operator P of order n in the interior and a trace operator T. In this particular situation, Dixmier's trace and the noncommutative residue do coincide up to a factor.

AB - Let X be a smooth manifold with boundary of dimension n > 1. The operators of order -n and type zero in Boutet de Monvel's calculus form a subset of Dixmier's trace ideal ℒ1,∞(H) for the Hilbert space H = L2(X, E) ⊕ L2(∂X, F) of L2 sections in vector bundles E over X, F over ∂X. We show that, on these operators, Dixmier's trace can be computed in terms of the same expressions that determine the noncommutative residue. In particular it is independent of the averaging procedure. However, the noncommutative residue and Dixmier's trace are not multiples of each other unless the boundary is empty. As a corollary we show how to compute Dixmier's trace for parametrices or inverses of classical elliptic boundary value problems of the form Pu = f; Tu = 0 with an elliptic differential operator P of order n in the interior and a trace operator T. In this particular situation, Dixmier's trace and the noncommutative residue do coincide up to a factor.

UR - http://www.scopus.com/inward/record.url?scp=0032375056&partnerID=8YFLogxK

U2 - 10.1007/s002290050062

DO - 10.1007/s002290050062

M3 - Journal article

AN - SCOPUS:0032375056

VL - 96

SP - 203

EP - 218

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 2

ER -

ID: 237365055