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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The essential spectrum of elliptic differential operators in $L^{p}(R_{n})$
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by Erik Balslev PDF
Trans. Amer. Math. Soc. 116 (1965), 193-217 Request permission
  • E. Balslev and T. W. Gamelin, The essential spectrum of a class of ordinary differential operators, Pacific J. Math. 14 (1964), 755–776. MR 171179, DOI 10.2140/pjm.1964.14.755
  • E. Balslev, Perturbation of differential operators, Ph.D. Thesis, Univ. of California, Berkeley, Calif., 1963.
  • M. Š. Birman, On the spectrum of singular boundary-value problems, Mat. Sb. (N.S.) 55 (97) (1961), 125–174 (Russian). MR 0142896
  • Inge Brinck, Self-adjointness and spectra of Sturm-Liouville operators, Math. Scand. 7 (1959), 219–239. MR 112999, DOI 10.7146/math.scand.a-10575
  • Felix E. Browder, On the spectral theory of elliptic differential operators. I, Math. Ann. 142 (1960/61), 22–130. MR 209909, DOI 10.1007/BF01343363
  • Felix E. Browder, Functional analysis and partial differential equations. II, Math. Ann. 145 (1961/62), 81–226. MR 136857, DOI 10.1007/BF01342796
  • Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745
  • I. C. Gohberg and M. G. Kreĭn, The basic propositions on defect numbers, root numbers and indices of linear operators, Amer. Math. Soc. Transl. (2) 13 (1960), 185–264. MR 0113146, DOI 10.1090/trans2/013/08
  • Teruo Ikebe and Tosio Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rational Mech. Anal. 9 (1962), 77–92. MR 142894, DOI 10.1007/BF00253334
  • Tosio Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261–322. MR 107819, DOI 10.1007/BF02790238
  • Nils Nilsson, Essential self-adjointness and the spectral resolution of Hamiltonian operators, Kungl. Fysiografiska Sällskapets i Lund Förhandlingar [Proc. Roy. Physiog. Soc. Lund] 29 (1959), no. 1, 1–19. MR 104901
  • G. C. Rota, Extension theory of differential operators. I, Comm. Pure Appl. Math. 11 (1958), 23–65. MR 96852, DOI 10.1002/cpa.3160110103
  • L. Schwartz, Théorie des distributions. II, Hermann, Paris, 1959.
  • František Wolf, On the essential spectrum of partial differential boundary problems, Comm. Pure Appl. Math. 12 (1959), 211–228. MR 107750, DOI 10.1002/cpa.3160120202
  • Fernando Roldão Dias Agudo and František Wolf, Propriétés spectrales de l’opérateur \[ {\partial ^2\over \partial x^2}+{\partial ^2\over \partial y^2}+{\partial ^2\over \partial z ^2}+a {\partial \over \partial x}+b{\partial \over \partial y}+ c{\partial \over \partial z}+d\] á coefficients complexes, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 25 (1958), 273–275 (French). MR 113026
  • E. Balslev and C. F. Schubert, Essential spectrum and singular sequences, Pacific J. Math. (to appear). E. Balslev, The essential spectrum of self-adjoint elliptic differential operators in ${L^2}({R_n})$, Math. Scand. (to appear).
  • P. A. Rejto, On the essential spectrum of the hydrogen energy and related operators, Pacific J. Math. 19 (1966), 109–140. MR 199574, DOI 10.2140/pjm.1966.19.109
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Additional Information
  • © Copyright 1965 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 116 (1965), 193-217
  • MSC: Primary 35.80; Secondary 47.65
  • DOI:
  • MathSciNet review: 0190524