Details
| Original language | English |
|---|---|
| Pages (from-to) | 561-602 |
| Number of pages | 42 |
| Journal | Publications of the Research Institute for Mathematical Sciences |
| Volume | 56 |
| Issue number | 3 |
| Publication status | Published - 18 Jun 2020 |
Abstract
We study Fourier integral operators with Shubin amplitudes and quadratic phase functions associated to twisted graph Lagrangians with respect to symplectic matrices. We factorize such an operator as the composition of a Weyl pseudodifferential operator and a metaplectic operator and derive a characterization of its Schwartz kernel in terms of phase space estimates. Extending the conormal distributions in the Shubin calculus, we define an adapted notion of Lagrangian tempered distribution. We show that the kernels of Fourier integral operators are identical to Lagrangian distributions with respect to twisted graph Lagrangians.
Keywords
- FBI transform, Fourier integral operator, Lagrangian distribution, Phase space analysis, Shubin amplitude
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Publications of the Research Institute for Mathematical Sciences, Vol. 56, No. 3, 18.06.2020, p. 561-602.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Lagrangian Distributions and Fourier Integral Operators with Quadratic Phase Functions and Shubin Amplitudes
AU - Schulz, René Marcel
AU - Wahlberg, Patrik
AU - Cappiello, Marco
N1 - Funding Information: We are grateful to Professor Fabio Nicola for helpful discussions. R. Schulz gratefully acknowledges support from the project “Fourier Integral Operators, Symplectic Geometry and Analysis on Noncompact Manifolds” received by the University of Turin in the form of an “I@Unito” fellowship, as well as institutional support by the University of Hannover.
PY - 2020/6/18
Y1 - 2020/6/18
N2 - We study Fourier integral operators with Shubin amplitudes and quadratic phase functions associated to twisted graph Lagrangians with respect to symplectic matrices. We factorize such an operator as the composition of a Weyl pseudodifferential operator and a metaplectic operator and derive a characterization of its Schwartz kernel in terms of phase space estimates. Extending the conormal distributions in the Shubin calculus, we define an adapted notion of Lagrangian tempered distribution. We show that the kernels of Fourier integral operators are identical to Lagrangian distributions with respect to twisted graph Lagrangians.
AB - We study Fourier integral operators with Shubin amplitudes and quadratic phase functions associated to twisted graph Lagrangians with respect to symplectic matrices. We factorize such an operator as the composition of a Weyl pseudodifferential operator and a metaplectic operator and derive a characterization of its Schwartz kernel in terms of phase space estimates. Extending the conormal distributions in the Shubin calculus, we define an adapted notion of Lagrangian tempered distribution. We show that the kernels of Fourier integral operators are identical to Lagrangian distributions with respect to twisted graph Lagrangians.
KW - FBI transform
KW - Fourier integral operator
KW - Lagrangian distribution
KW - Phase space analysis
KW - Shubin amplitude
UR - http://www.scopus.com/inward/record.url?scp=85090742151&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1802.04729
DO - 10.48550/arXiv.1802.04729
M3 - Article
VL - 56
SP - 561
EP - 602
JO - Publications of the Research Institute for Mathematical Sciences
JF - Publications of the Research Institute for Mathematical Sciences
SN - 0454-7845
IS - 3
ER -