• Corpus ID: 239024534

# $L^p$-bounds for eigenfunctions of analytic non-self-adjoint operators with double characteristics

@inproceedings{White2021LpboundsFE,
title={\$L^p\$-bounds for eigenfunctions of analytic non-self-adjoint operators with double characteristics},
author={Francis White},
year={2021}
}
• F. White
• Published 19 October 2021
• Mathematics, Physics
We prove sharp uniform L-bounds for low-lying eigenfunctions of non-self-adjoint semiclassical pseudodifferential operators P on R whose principal symbols are doubly-characteristic at the origin of R. Our bounds hold under two main assumptions on P : (1) the total symbol of P extends holomorphically to a tubular neighborhood of R in C, and (2) the quadratic approximation to the principal symbol of P at the origin is elliptic along its singular space. Most notably, our assumptions on the…

## References

SHOWING 1-10 OF 47 REFERENCES
Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics
• Mathematics
• 2011
For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in
Semiclassical Hypoelliptic Estimates for Non-Selfadjoint Operators with Double Characteristics
• Mathematics
• 2009
For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, with a leading symbol with a non-negative real part, we study bounds for resolvents and
Subelliptic estimates for quadratic differential operators
We prove global subelliptic estimates for quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a
From semigroups to subelliptic estimates for quadratic operators
• Mathematics
• 2015
Using an approach based on the techniques of FBI transforms, we give a new simple proof of the global subelliptic estimates for non-selfadjoint non-elliptic quadratic differential operators, under a
Spectra and semigroup smoothing for non-elliptic quadratic operators
• Mathematics
• 2007
We study non-elliptic quadratic differential operators. Quadratic differential operators are non-selfadjoint operators defined in the Weyl quantization by complex-valued quadratic symbols. When the
Spectral asymptotics in the semi-classical limit
• Mathematics
• 1999
Introduction 1. Local symplectic geometry 2. The WKB-method 3. The WKB-method for a potential minimum 4. Self-adjoint operators 5. The method of stationary phase 6. Tunnel effect and interaction
Spectral projections and resolvent bounds for partially elliptic quadratic differential operators
We study resolvents and spectral projections for quadratic differential operators under an assumption of partial ellipticity. We establish exponential-type resolvent bounds for these operators,
Spectral Analysis of a Complex Schrödinger Operator in the Semiclassical Limit
• Mathematics, Physics
SIAM J. Math. Anal.
• 2016
For a one dimensional setting, the Dirichlet realization of the operator-h^2\Delta+iV in the semi-classical limit $h\to0$ is considered, and the complete asymptotic expansion, in powers of $h$, of each eigenvalue is obtained.