Fractional powers of elliptic differential operators
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 3, Volume 22 (1968) no. 1, p. 113-132 
@article{ASNSP_1968_3_22_1_113_0,
     author = {Burak, Tamar},
     title = {Fractional powers of elliptic differential operators},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 22},
     number = {1},
     year = {1968},
     pages = {113-132},
     zbl = {0159.15601},
     mrnumber = {236767},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1968_3_22_1_113_0}
}

Burak, Tamar. Fractional powers of elliptic differential operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 3, Volume 22 (1968) no. 1, pp. 113-132. http://www.numdam.org/item/ASNSP_1968_3_22_1_113_0/

[1] S. Agmon: On the eigenfunctions and on the eigenvalues of elliptic boundary value problems, Comm. Pure Appl. Math. Vol. 15, pp. 119-147 (1962). | MR 147774 | Zbl 0109.32701

[2] S. Agmon: Lectures on elliptic boundary value problems. Van-Nostrand Mathematical Studies. Princeton N. J. 1965. | MR 178246 | Zbl 0142.37401

[3] S. Agmon: On kernels eigenvalues and eigenfunctions of operators related to elliptic problems. Comm. Pure Appl. Math. Vol. 18, pp. 627-663 (1965). | MR 198287 | Zbl 0151.20203

[4] T. Burak: Pseudodifferential operators depending on a parameter and fractional powers of elliptic differential operators. Thesis. Hebrew University of Jerusalem. (1967).

Dunford-Schwartz : [5] Linear operators II.

[6] T. Kato: Note on fractional powers of linear operators. Proc. Japan Acad. Vol. 36, pp. 94-96 (1960). | MR 121666 | Zbl 0097.31802

[7] J.J. Kohn and L. Nirenberg: An algebra of pseudodifferential operators. Comm. Pure Appl. Math. Vol. 18, pp. 267-305 (1965). | Zbl 0171.35101

[8] T. Kotaké and M.S. Narasimhan: Regutarity theorems for fractional powers of a linear elliptic operator. Bull. Soc. Math. France. Vol. 90, pp. 449-471 (1962). | Numdam | MR 149329 | Zbl 0104.32503

[9] S. Minakshundaram and A. Pleijel: Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds. Canadian Journal of Mathematics. Vol. I, pp. 242-256 (1949). | MR 31145 | Zbl 0041.42701

[10] R.S. Palais: Seminar on the Atiyah-Singer index theorem. Annals of Mathematics. Studies No. 5.7.

[11] R.T. Seeley: The powers As of an elliptic operator A. To be published.