Abstract
In this paper, we expand on B.-W. Schulze’s abstract edge pseudodifferential calculus and introduce a larger class of operators that is modeled on Hörmander’s ρ, δ calculus, where 0 ≤ δ < ρ ≤ 1. This expansion is motivated by recent work on boundary value problems for elliptic wedge operators with variable indicial roots by G. Mendoza and the author, where operators of type 1, δ for 0 < δ < 1 appear naturally. Some of the results of this chapter also represent improvements over the existing literature on the standard abstract edge calculus of operators of type 1, 0, such as trace class mapping properties of operators in abstract wedge Sobolev spaces. The presentation in this paper is largely self-contained to allow for an independent reading.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 179-207 |
| Number of pages | 29 |
| Journal | Springer Proceedings in Mathematics and Statistics |
| Volume | 119 |
| DOIs | |
| State | Published - Jan 1 2015 |
| Event | International Workshop on Elliptic and Parabolic Equations, 2013 - Hannover, Germany Duration: Sep 10 2013 → Sep 12 2013 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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A calculus of abstract edge pseudodifferential operators of type ρ, δ. / Krainer, Thomas.
In: Springer Proceedings in Mathematics and Statistics, Vol. 119, 01.01.2015, p. 179-207.Research output: Contribution to journal › Conference article
TY - JOUR
T1 - A calculus of abstract edge pseudodifferential operators of type ρ, δ
AU - Krainer, Thomas
PY - 2015/1/1
Y1 - 2015/1/1
N2 - In this paper, we expand on B.-W. Schulze’s abstract edge pseudodifferential calculus and introduce a larger class of operators that is modeled on Hörmander’s ρ, δ calculus, where 0 ≤ δ < ρ ≤ 1. This expansion is motivated by recent work on boundary value problems for elliptic wedge operators with variable indicial roots by G. Mendoza and the author, where operators of type 1, δ for 0 < δ < 1 appear naturally. Some of the results of this chapter also represent improvements over the existing literature on the standard abstract edge calculus of operators of type 1, 0, such as trace class mapping properties of operators in abstract wedge Sobolev spaces. The presentation in this paper is largely self-contained to allow for an independent reading.
AB - In this paper, we expand on B.-W. Schulze’s abstract edge pseudodifferential calculus and introduce a larger class of operators that is modeled on Hörmander’s ρ, δ calculus, where 0 ≤ δ < ρ ≤ 1. This expansion is motivated by recent work on boundary value problems for elliptic wedge operators with variable indicial roots by G. Mendoza and the author, where operators of type 1, δ for 0 < δ < 1 appear naturally. Some of the results of this chapter also represent improvements over the existing literature on the standard abstract edge calculus of operators of type 1, 0, such as trace class mapping properties of operators in abstract wedge Sobolev spaces. The presentation in this paper is largely self-contained to allow for an independent reading.
UR - http://www.scopus.com/inward/record.url?scp=84931339016&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84931339016&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-12547-3_8
DO - 10.1007/978-3-319-12547-3_8
M3 - Conference article
VL - 119
SP - 179
EP - 207
JO - Springer Proceedings in Mathematics and Statistics
JF - Springer Proceedings in Mathematics and Statistics
SN - 2194-1009
ER -