# On the eigenvalues of a class of hypo-elliptic operators. IV

Annales de l'institut Fourier (1980)

- Volume: 30, Issue: 2, page 109-169
- ISSN: 0373-0956

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topSjöstrand, Johannes. "On the eigenvalues of a class of hypo-elliptic operators. IV." Annales de l'institut Fourier 30.2 (1980): 109-169. <http://eudml.org/doc/74446>.

@article{Sjöstrand1980,

abstract = {Let $P$ be a selfadjoint classical pseudo-differential operator of order $>1$ with non-negative principal symbol on a compact manifold. We assume that $P$ is hypoelliptic with loss of one derivative and semibounded from below. Then exp$(-tP)$, $t\ge 0$, is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of $P$ is computed. This paper is a continuation of a series of joint works with A. Menikoff.},

author = {Sjöstrand, Johannes},

journal = {Annales de l'institut Fourier},

keywords = {non-classical Fourier integral operator; asymptotic distribution of eigenvalues},

language = {eng},

number = {2},

pages = {109-169},

publisher = {Association des Annales de l'Institut Fourier},

title = {On the eigenvalues of a class of hypo-elliptic operators. IV},

url = {http://eudml.org/doc/74446},

volume = {30},

year = {1980},

}

TY - JOUR

AU - Sjöstrand, Johannes

TI - On the eigenvalues of a class of hypo-elliptic operators. IV

JO - Annales de l'institut Fourier

PY - 1980

PB - Association des Annales de l'Institut Fourier

VL - 30

IS - 2

SP - 109

EP - 169

AB - Let $P$ be a selfadjoint classical pseudo-differential operator of order $>1$ with non-negative principal symbol on a compact manifold. We assume that $P$ is hypoelliptic with loss of one derivative and semibounded from below. Then exp$(-tP)$, $t\ge 0$, is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of $P$ is computed. This paper is a continuation of a series of joint works with A. Menikoff.

LA - eng

KW - non-classical Fourier integral operator; asymptotic distribution of eigenvalues

UR - http://eudml.org/doc/74446

ER -

## References

top- [1] L. HÖRMANDER, A class of hypoelliptic pseudodifferential operators with double characteristics, Math. Ann., 217 (1975), 165-188. Zbl0306.35032MR51 #13774
- [2] J. KARAMATA, Neuer Beweis und Verallgemeinerung der Tauberschen Sätze etc., J. Reine u. Angew. Math., 164 (1931), 27-39. Zbl0001.27302JFM57.0262.01
- [3] A. MELIN, Lower bounds for pseudo-differential operators, Ark. f. Math., 9 (1971), 117-140. Zbl0211.17102MR48 #6735
- [4] A. MELIN and J. SJÖSTRAND, Fourier integral operators with complex phase functions and parametrix for an interior boundary value problem, Comm. P.D.E., 1 (1976), 313-400. Zbl0364.35049MR56 #13294
- [5] A. MELIN and J. SJÖSTRAND, A calculus for Fourier integral operators in domains with boundary and applications to the oblique derivative problem, Comm. P.D.E., 2 (1977), 857-935. Zbl0392.35055MR56 #16708
- [6] A. MENIKOFF and J. SJÖSTRAND, On the eigenvalues of a class of hypoelliptic operators, Math. Ann., 235 (1978), 55-85. Zbl0375.35014MR58 #1735
- [7] A. MENIKOFF and J. SJÖSTRAND, On the eigenvalues of a class of hypoelliptic operators II, Springer L. N., n°755, 201-247. Zbl0444.35019MR82m:35114
- [8] A. MENIKOFF and J. SJÖSTRAND, The eigenvalues of hypoelliptic operators, III, the non semibounded case, Journal d'Analyse Math., 35 (1979), 123-150. Zbl0436.35065
- [9] J. SJÖSTRAND, Eigenvalues for hypoelliptic operators and related methods, Proc. Inter. Congress of Math., Helsinki, 1978, 445-447.

## Citations in EuDML Documents

top- Bernard Lascar, Johannes Sjöstrand, Équation de Schrödinger et propagation des singularités. II
- C. Fefferman, D. H. Phong, Pseudo-differential operators with positive symbols
- Abderemane Mohamed, Étude spectrale d'opérateurs hypoelliptiques à caractéristiques multiples
- Abderemane Mohamed, Étude spectrale d'opérateurs hypoelliptiques à caractéristiques multiples. I

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