Abstract
The theory of analytic pseudo-differential operators (hereafter abbreviated as ψDOs) started with [BKr67]. The interest of Professor Boutet de Monvel in analyticity is characteristic in his research, and it is remarkable as “regularity” normally meant C ∞ in 1960s. The results of this paper are effectively used in his thesis [B69] to construct the parametrix for the elliptic boundary value problem in C ω-framework.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Louis Boutet de Monvel and Paul Krée, Pseudo-differential operators and Gevrey classes, Ann. Inst. Fourier (Grenoble) 17 (1967), no. 1, 295–323.
L. Boutet de Monvel, Opérateurs pseudo-différentiels analytiques et problèmes aux limites elliptiques, Ann. Inst. Fourier (Grenoble) 19 (1969), no. 2, 169–268.
L. Boutet de Monvel, Opérateurs pseudo-différentiels analytiques et opérateurs d’ordre infini, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 3, 229–268.
L. Boutet de Monvel, \(\mathcal{D}\) -modules holonômes réguliers en une variable, Mathematics and physics (Paris, 1979/1982), Progr. Math., vol. 37, Birkhäuser Boston, Boston, MA, 1983, pp. 313–321.
L. Boutet de Monvel and B. Malgrange, Le théorème de l’indice relatif, Ann. Sci. École Norm. Sup. (4) 23 (1990), no. 1, 151–192.
L. Boutet de Monvel, Formal norms and star-exponentials, Lett. Math. Phys. 83 (2008), no. 3, 213–216.
T. Aoki, Invertibility for microdifferential operators of infinite order, Publ. Res. Inst. Math. Sci. 18 (1982), no. 2, 421–449.
S. Kamimoto, T. Kawai and T. Koike, Resurgent functions and linear differential operators of infinite order – Their happy marriage in exact WKB analysis, RIMS Kôkyûroku Bessatsu, Vol. B.52 (2014), 127–146.
M. Kashiwara and T. Kawai, On holonomic systems of micro-differential equations. III. – Systems with regular singularities –, Publ. Res. Inst. Math. Sci. 17 (1981), no. 3, 813–979.
M. Sato, T. Kawai and M. Kashiwara, Microfunctions and pseudo-differential equations. Hyperfunctions and pseudo-differential equations, (Proc. Conf., Katata, 1971; dedicated to the memory of André Martineau), pp. 265–529. Lecture Notes in Math., Vol. 287, Springer, Berlin, 1973.
L. Boutet de Monvel, \(\mathcal{D}\) -modules holonômes réguliers en une variable, Mathematics and physics (Paris, 1979/1982), Progr. Math., vol. 37, Birkhäuser Boston, Boston, MA, 1983, pp. 313–321.
L. Boutet de Monvel and B. Malgrange, Le théorème de l’indice relatif, Ann. Sci. École Norm. Sup. (4) 23 (1990), no. 1, 151–192.
L. Boutet de Monvel, Formal norms and star-exponentials, Lett. Math. Phys. 83 (2008), no. 3, 213–216.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Kawai, T. (2017). Analytic Pseudodifferential Operators. In: Guillemin, V., Sjöstrand, J. (eds) Louis Boutet de Monvel, Selected Works. Contemporary Mathematicians. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-27909-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-27909-1_5
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-27907-7
Online ISBN: 978-3-319-27909-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)