A characterization of the non local boundary value problems associated with an elliptic operator
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 3, Volume 22 (1968) no. 3, p. 425-513
@article{ASNSP_1968_3_22_3_425_0,
     author = {Grubb, Gerd},
     title = {A characterization of the non local boundary value problems associated with an elliptic operator},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 22},
     number = {3},
     year = {1968},
     pages = {425-513},
     zbl = {0182.14501},
     mrnumber = {239269},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1968_3_22_3_425_0}
}
Grubb, Gerd. A characterization of the non local boundary value problems associated with an elliptic operator. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 3, Volume 22 (1968) no. 3, pp. 425-513. http://www.numdam.org/item/ASNSP_1968_3_22_3_425_0/

[1] S. Agmon, A. Douglis and L. Nirenberg: Estimates near the boundary of solutions of elliptic partial differential equations satisfying general boundary conditions I. Comm. Pare Appl. Math. 12 (1959), 623-727. | MR 125307 | Zbl 0093.10401

[2] M.S. Agranovich and A.S. Dynin: General boundary value problems for elliptic systems in an n-dimensional domain. Dokl. Akad. Nauk SSSR 146 (1962), 511-514; Soviet Math. 3 (1962), 1323-1327. | MR 140820 | Zbl 0132.35403

[3] N. Aronszajn and A.N. Milgram: Differential operators on Riemannian manifolds. Rend. Circolo Mat. Palermo 2 (1952), 1-61. | MR 64255 | Zbl 0053.06502

[4] W.G. Bade and R.S. Freeman: Closed extensions of the Laplace operator determined by a general class of boundary conditions. Pacific J. Math. 12 1962, 395-410. | MR 165132 | Zbl 0198.17403

[5] R.W. Beals: Non-local boundary value problems for elliptio partial differential operators. Dissertation, Yale University 1964. | MR 2619391

[6] R.W. Beals: Non-local boundary value problems for elliptic operators. Amer. J. Math. 87 (1965), 315-362. | MR 182802 | Zbl 0134.31302

[7] M.S. Birman: On the theory of self-adjoint extensions of positive definite operators. Mat. Sbornik 38 (80) (1956), 431-450. finite operators. Mat. | MR 80271 | Zbl 0070.12102

[8] M.S. Birman: Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions. Vestnik Leuingrad Univ. 17, no. 1 (1962), 22-55. | MR 138874 | Zbl 0149.31903

[9] J.W. Calkin: Symmetric transformations in Hilbert space. Duke Math. Journal 7 (1940), 504-508. | JFM 66.0550.04 | MR 3466 | Zbl 0024.12301

[10] J. Ercolano and M. Schechter: Spectral theory for operators generated by elliptic boundary problems with eigenvalue parameter in boundary conditions (I). Comm. Pure Appl. Math. 18 (1965), 83-106. | MR 177313 | Zbl 0138.36201

[12] R.S. Freeman: Closed operators and their aadjoints associated with elliptic differential operators. Pacific J. Math. 22 (1967). 71-97. | MR 216335 | Zbl 0168.08405

[13] K.O. Friedrichs: Spektraltheorie halbbeschränkter Operatoren und Anvendung auf die Spektralzerlegung von Differentialoperatoren. Math. Ann. 109 (1934), 465-487. | JFM 60.1078.01 | MR 1512905

[14] K.O. Friedrichs: On the differentiability of the solutions of linear elliptic differential operators. Comm. Pure Appl. Math. 6, (1953), 299-326. | MR 58828 | Zbl 0051.32703

[15] G. Grubb: A characterization of the non-local boundary value problems associated with an elliptic operator. Dissertation, Stanford University, 1966. | MR 2615956

[16] E. Hille and R.S. Phillips: Functioraal Analysis and Semi Groups. Revised edition. Amer. Math. Soc. Colloq. Publ. 31 (1957). | MR 89373 | Zbl 0078.10004

[17] L. Hörmander: Definitions of maximal differential operators. Arkiv för Mat. 3 (1958), 501-404. | MR 106333 | Zbl 0131.09403

[18] L. Hörmander: Linear Partial Differential Operators. Springer-Verlag 1963. | MR 161012 | MR 404822 | Zbl 0108.09301

[19] L. Hörmander: Pseudo differential operators. Comm. Pure Appl. Math. 18 (1965), 501-518. | MR 180740 | Zbl 0125.33401

[20] T. Kato: Perturbactions of continuous spectra by trace class operators. Proc. Japan Acad. 33 (1957), 260-264. | MR 92133 | Zbl 0090.33101

[21] J.J. Kohn and L. Nirenberg: An algebra of pseudo differential operators. Comm. Pure Appl. Math. 18 (1965), 269-308 | MR 176362 | Zbl 0171.35101

[22] M.G. Krein: Theory of selfadjoint extensions of symmetric semi-bounded operators and applications (I). Mat. Sbornik 20 (62) (1947), 431-495. | MR 24574 | Zbl 0029.14103

[23] J.L. Lions: Equations différentielles opérationnelles et problèmes aux limites. Springer-Verlag 1961. | MR 153974 | Zbl 0098.31101

[24] J.L. Lions and E. Magenes: Problemi ai limiti non omogenei; (I), (III), (IV), (V): Annali Scuola Norm. Pisa, 14 (1960), 259-308; 16 (1961), 39-101, 311-326; 16 (1962), 1-44; - Problèmes aux limites non homogènes ; (II): Annales Inst. Fourier (Grenoble) 11 (1961), 137-178; (VI) : J. d'Analyse Math. 11 (1963), 165-188. | Numdam | MR 146525 | Zbl 0095.30303

[24'] J.L. Lions and E. Magenes: Problèmes aux limites non homogènes et applications, Vol. I Ed. Dunod. Paris 1968. | Zbl 0165.10801

[25] R.S. Phillips: Dissipative operators and hyperbolic systems of partial differential equations. Trans. Amer. Math. Soc. 90 (1959), 193-254. | MR 104919 | Zbl 0093.10001

[26] F. Riesz and B. Sz.-Nagy: Lecons d'analyse fonctionnelle. Académie des Sci. de Hongrie, Akadémiai Kradó, Budapest 1953. | MR 56821 | Zbl 0046.33103

[27] M., Rosenblum: Perturbations of the continuous spectrum and unitary equivalence. Pacific J. Math. 7 (1957), 997-1010. | MR 90028 | Zbl 0081.12003

[28] M. Schechter: General boundary value problems for elliptic differential equations. Comm. Pure A ppl. Math. 12 (1959), 457-486. | MR 125323 | Zbl 0087.30204

[29] M. Schechter: Nonlocal elliptic boundary value problems. Ann. Scuola Norm. Sup. Pisa 20 (1966), 421-441. | Numdam | MR 197987 | Zbl 0152.11005

[30] M.H. Stone: Linear Transfomations in Hilbert Space and their Applications to Analysis. Amer. Math. Soc. Colloq. Publ. 15 (1932) (reprinted 1951). | JFM 58.0420.02 | MR 1451877

[31] S.V. Uspenskii: Properties of the classes Wrp with a frational derivative on differential manifolds. Dokl. Akad. Nauk 132 (1960), 60-62. | MR 124732 | Zbl 0103.08204

[32] I.M. Vishik: On general boundary value problems for elliptic differential equations. Trudy Mosc. Mat. Obsv. 1 (1952), 187-246; Amer. Math. Soc. Transl. (2) 24, (1963), 107-172 | MR 51404 | Zbl 0131.32301