Topic
Trace operator
About: Trace operator is a research topic. Over the lifetime, 1233 publications have been published within this topic receiving 20796 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 1977
TL;DR: A family of semi-norms is defined, subject to some interpolating conditions, providing interpolation methods that preserve polynomials of degree≤m−1 and converge in Sobolev spaces Hm+s(Ω).
Abstract: We define a family of semi-norms ‖μ‖m,s=(∫ℝ n∣τ∣2s∣ℱ Dmu(τ)∣2 dτ)1/2 Minimizing such semi-norms, subject to some interpolating conditions, leads to functions of very simple forms, providing interpolation methods that: 1°) preserve polynomials of degree≤m−1; 2°) commute with similarities as well as translations and rotations of ℝn; and 3°) converge in Sobolev spaces Hm+s(Ω).
1,702 citations
Book•
1 Jan 1996
1,427 citations
TL;DR: In this paper, the symbolic calculus is developed further than in [6], and an index formula for elliptic problems, extending the results of [3] and [6] is derived.
Abstract: which will contain at least the operator describing a classical boundary problem, and also i ts parametr ix in the elliptic case. In fact what we construct there is one of the smallest possible \"algebras\" tha t will work. In tha t respect, our result is less general than tha t of Vi~ik and Eskin [10]. The difference lies in the fact tha t in our problem, the pseudo-differential appearing in (0.1) (coefficient A) has to satisfy a supplementary condition along the boundary: the transmission property. (1) The operators tha t arise in (0.1) have already been described in [6] (where we also require analyticity). In this work, we only require tha t the operators preserve locally Coo functions. The symbolic calculus is developed further than in [6], and we derive an index formula for elliptic problems, extending tha t of [3]. Roughly speaking, the coefficient A in (0.1)is a sum A = P + G , whereP is a pseudodifferential operator satisfying the transmission condition (w 2), and G (which we call a singular Green operator -w 3) is an operator which takes any distribution into a function which is C ~ inside ~ (but may be irregular at the boundary): such operators arise for
619 citations
TL;DR: In this paper, continuity for weighted modulation spaces is discussed, and it is shown that many such spaces can be obtained in a canonical way from the corresponding standard modulation spaces, and the trace operator a↦a(0, ·) acting on modulationspaces.
425 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 3 |
| 2023 | 11 |
| 2022 | 20 |
| 2021 | 7 |
| 2020 | 12 |