## Arkiv för Matematik

• Ark. Mat.
• Volume 55, Number 1 (2017), 243-270.

### Spectral analysis of the subelliptic oblique derivative problem

Kazuaki Taira

#### Abstract

This paper is devoted to a functional analytic approach to the subelliptic oblique derivative problem for the usual Laplacian with a complex parameter $\lambda$. We solve the long-standing open problem of the asymptotic eigenvalue distribution for the homogeneous oblique derivative problem when $\lvert \lambda \rvert$ tends to $\infty$. We prove the spectral properties of the closed realization of the Laplacian similar to the elliptic (non-degenerate) case. In the proof we make use of Boutet de Monvel calculus in order to study the resolvents and their adjoints in the framework of $L^2$ Sobolev spaces.

#### Article information

Source
Ark. Mat., Volume 55, Number 1 (2017), 243-270.

Dates
First available in Project Euclid: 2 February 2018

https://projecteuclid.org/euclid.afm/1517535612

Digital Object Identifier
doi:10.4310/ARKIV.2017.v55.n1.a13

Mathematical Reviews number (MathSciNet)
MR3711152

Zentralblatt MATH identifier
06823283

#### Citation

Taira, Kazuaki. Spectral analysis of the subelliptic oblique derivative problem. Ark. Mat. 55 (2017), no. 1, 243--270. doi:10.4310/ARKIV.2017.v55.n1.a13. https://projecteuclid.org/euclid.afm/1517535612