On the essential spectrum of the hydrogen energy and related operators.
P. A. Rejto
Source: Pacific J. Math. Volume 19, Number 1
(1966), 109-140.
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Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102993960
Zentralblatt MATH identifier: 0144.17701
Mathematical Reviews number (MathSciNet): MR0199574
References
[1] F. R. D. Agudo and F. Wolf, Propretes spectrales des equations differentielles non- autoadjoints, Rend. Acad. Naz. Lincei 24, (1958), 643-645.
Mathematical Reviews (MathSciNet): MR20:7127
Zentralblatt MATH: 0084.33803
[2] F. R. D. Agudo and F. Wolf,Proprietes spectrales de operateur dx2dy2dz2dxdydz a coefficients complexes, Rend. Acad. Naz. Lincei. 25 (1958), 273-275.
Mathematical Reviews (MathSciNet): MR22:3867
Zentralblatt MATH: 0084.09304
[3] N. Aronszajn, On coercive integro-differentialquadratic forms,Conference on Partial Differential Equations, University of Kansas, 1954.
[4] G. S. Avila and C. H. Wilcox, The propagation of time harmonic waves in homo- genious anisotropic media, MRC Technical Summary Report (to appear).
[5] E. Balslev, The essential spectrum of elliptic differentialoperators in Lp(Rn)(to appear, Trans. Amer. Math. Soc.)
Mathematical Reviews (MathSciNet): MR32:7936
Zentralblatt MATH: 0148.09403
[6] E. Balslev, The essential spectrum of self adjoint elliptic differential operators in LKRn) (to appear, Math. Scand.)
[7] E. Balslev,Perturbation of ordinary differentialoperators, Math. Scand. 11 (1962) 131-148.
Mathematical Reviews (MathSciNet): MR28:490
Zentralblatt MATH: 0196.44501
[8] E. Balslev, Pacific J. Math. (1964)
[9] M. Sh. Birman, On the spectrum of singular boundary value problems, (Russian), Mat. Sbor. 97 (1961) 125-174. Math. Rev. 26 (1963), No.463.
Mathematical Reviews (MathSciNet): MR26:463
[10] M. Sh. Birman, Perturbations of continuous spectra of singular elliptic operators under the change of boundary and boundary conditions (Russian), Vestnik Leningradskovo Universiteta, Ser. Mat. Mech. Ast. (1962), 22-55. Math. Rev. 25 (1963) No.2314.
Mathematical Reviews (MathSciNet): MR25:2314
[11] M. Sh. Birman, On the theory of wave operators, andscattering operators, Doklady Akad. Nauk SSSR 144 (1962),475-478. Transl. Soviet Math. Dokl.,
Mathematical Reviews (MathSciNet): MR25:2447
Zentralblatt MATH: 0196.45004
[12] F. E. Browder, On the spectral theory of elliptic differentialoperators I, Math. Annalen 142 (1961), 22-130.
Mathematical Reviews (MathSciNet): MR35:804
Zentralblatt MATH: 0104.07502
[13] F. H. Brownell, A note on Cook's wave matrix theorem, Pacific J. Math. 12 (1962), 47-52.
Mathematical Reviews (MathSciNet): MR26:1055
Zentralblatt MATH: 0103.44902
[14] F. H. Brownell, Perturbation of the n-dimensional Schrdinger differential operator, Bull. Amer. Math. Soc. (1954), No. 430.
[15] F. H. Brownell,Spectrum of the static potential Schrdingerequation over En, Ann. of Math. 54 (1951), 554-594.
Mathematical Reviews (MathSciNet): MR13:847a
Zentralblatt MATH: 0044.42703
[16] J. W. Calkin, Two sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. 42 (1941),839-873.
Mathematical Reviews (MathSciNet): MR3:208c
Zentralblatt MATH: 0063.00692
[17] Courant-Hilbert, Methods of mathematical physics, Vol. 2, Interscience Publishers, New York, 1962.
Zentralblatt MATH: 0099.29504
[18] L. de Branges, Perturbations of self-adjoint transformations,Amer. J. Math. 84 (1962), 543-560.
Mathematical Reviews (MathSciNet): MR27:4083
Zentralblatt MATH: 0134.11801
[19] N. Dunford and J. Schwartz,Linear operators Parts I and II, Chapters I-VIII and IX-XX respectively, Interscience Publishers, New York, 1957 and 1963.
Mathematical Reviews (MathSciNet): MR32:6181
Zentralblatt MATH: 0128.34803
[20] K. O. Friedrichs, Spectral theory of operators in Hilbert space, N. Y. U. Lecture Notes, 1959-60.
Zentralblatt MATH: 0266.47001
[21] K. O. Friedrichs, Well poseddifferential equation problems in mathematical physics, N.Y. U. Lecture notes, 1963.
[22] I. M. Glazman, On the application of the method of splittingtomultidimensional singular boundary value problems, (Russian), Mat. Sbor. 35 (1954) 231-246. Math. Rev. 16 (1955), 827.
Mathematical Reviews (MathSciNet): MR16:827c
[23] I. M. Glazman, On the spectra of ordinary, linear, singularboundary value problems, (Russian), Doklady Akad Nauk SSSR 87 (1952) 5-8. Math. Rev. 14 (1953), 1088.
[24] I. C. Gokhberg and M. G. Krein, Basic propositions on deficiency numbers, root numbers, and indices of linear operators, (Russian), Upspehi Matem. Nauk 12 (1957), 43-118. Amer. Math. Soc. Transl. (2) 13 (1960) 185-264.
Mathematical Reviews (MathSciNet): MR22:3984
[25] L. Hrmander, Estimates for translation invariant operators in Lp spaces, Acta. Mat. 104 (1960) 95-140.
[26] L. Hrmander, Linear partial differential operators, Springer Verlag, 1963.
Zentralblatt MATH: 0108.09301
[27] F. John, Plane waves and spherical means, Interscience Tracts in Pure and Appl. Math. No. 2, New York, 1955.
Mathematical Reviews (MathSciNet): MR17:746d
Zentralblatt MATH: 0067.32101
[28] K. Jrgens, Wesentliche Selbstadjungiertheitsinguldrerelliptisherdifferential- operatoren zweiter ordnung in CTM(G),Math. Scand. 15 (1964) 5-17.
[29] T. Kato, Fundamental properties of Hamiltonian operators of Schrdinger type, Trans. Amer. Math. Soc. 70 (1951) 196-211.
Mathematical Reviews (MathSciNet): MR12:781a
Zentralblatt MATH: 0044.42701
[30] T. Kato, On the convergence of the perturbation method, Journal, Science Faculty,
Zentralblatt MATH: 0045.21602
[31] T. Kato, Uniqueness of the self-adjoint extensions of singular elliptic differential operators, Archive Rat. Mech. Anal. 9, (1962), 77-92.
Mathematical Reviews (MathSciNet): MR26:461
Zentralblatt MATH: 0103.31801
[32] P. D. Lax and R. Phillips, Local boundary conditions for dissipativesymmetric linear differential operators, Comm. Pure Appl. Math. 13 (1960) 427-455.
Mathematical Reviews (MathSciNet): MR22:9718
Zentralblatt MATH: 0094.07502
[33] B. J. McLeod, On the continuous spectra of small potentials, (appear, Quart. J. Math., Oxford)
Mathematical Reviews (MathSciNet): MR31:6124
Zentralblatt MATH: 0128.32704
[34] A. M. Molchanov, Discreteness criteria for self adjoint second orderdifferential operators, (Russian), Trudy Mockovskovo Mat. Obshestvo. 2 (1953) 169-200.
[35] P. A. Rejto, On the essential spectrum of the hydrogen energy operator, Math. Res. Ctr. Technical Summary Report 540, Madison, 1965.
Mathematical Reviews (MathSciNet): MR33:7717
Zentralblatt MATH: 0144.17701
[36] F. Riesz and B. Sz. Nagy, Functional analysis, Translation, Frederick Ungar Co., New York, 1955.
Mathematical Reviews (MathSciNet): MR17:175i
[37] M. Schechter, Invariance of the essential spectrum, Bull. Amer. Math. Soc. 71 (1965), 365-367.
Mathematical Reviews (MathSciNet): MR30:5167
Zentralblatt MATH: 0132.35605
[38] M. Schechter, On estimating elliptic partial differential operators in the Lz norm, Amer. J. Math. 79 (1957).
Mathematical Reviews (MathSciNet): MR19:555b
Zentralblatt MATH: 0079.11701
[39] J. Schwartz, Some results on the spectra and spectral resolutions of a class of singular integral operators, Comm. Pure Appl. Math. 15 (1962) 75-90.
Mathematical Reviews (MathSciNet): MR29:480
Zentralblatt MATH: 0111.30202
[40] S. L. Sobolev, Application of functional analysis in mathematical physics. Trans- lations of Math. Monographs, Vol. 7, A. M. S. 1963.
Mathematical Reviews (MathSciNet): MR26:6758
[41] F. Stummel, Singulare elliptische Differentialoperatorenin Hilbertschen Rdumen, Math. Annalen 132 (1956), 150-176.
Mathematical Reviews (MathSciNet): MR19:283c
[42] E. C. Titchmarsh, Eigenfunctionexpansions associated with second order differ- ential equations, Clarendon Press, Oxford, 1946.
Mathematical Reviews (MathSciNet): MR8:458d
Zentralblatt MATH: 0061.13505
[43] E. Wienholtz, Halbbeschrdnkte partielle differentialoperatorenzweiterordnung vom elliptischen typus, Math. Annalen 135 (1958) 51.
Mathematical Reviews (MathSciNet): MR20:1090
Zentralblatt MATH: 0142.37701
[44] F. Wolf, On the essential spectrum of partial differential boundary problems, Comm. Pure Appl. Math. 12 (1959),211-228.
Mathematical Reviews (MathSciNet): MR21:6472
Zentralblatt MATH: 0087.30501
[45] F. Wolf,On the invariance of the essential spectrum under a change of boundary conditions of partial differentialoperators, Proc. Konikl. Ned. Akad. Wet. (A) 62 (1959), 142-147.
Mathematical Reviews (MathSciNet): MR21:6473
Zentralblatt MATH: 0086.08203
[46] F. Wolf,On the perturbationof an elliptic operator which leaves the essential spectrum invariant, Bull. Acad. Belg. 46 (1960) 441-447.
Mathematical Reviews (MathSciNet): MR23:A414
Zentralblatt MATH: 0097.30501
[47] F. Wolf, On singular partial differential boundary problems, Ann. di Mat. Pura ed Applicada 69 (1960) 167-180.
Mathematical Reviews (MathSciNet): MR22:2783
Zentralblatt MATH: 0133.05102
[48] B. Yood, Properties of linear transformationspreserved under addition of a completly continuous transformation,Duke Math. J. 18 (1951) 599-612.
Mathematical Reviews (MathSciNet): MR13:355f
Zentralblatt MATH: 0043.11901
[49] M. G. Zhiclin, On the spectrumof the many particleSchrdingeroperator, (Russian), Trudy Mockovskovo Mat. Obshestvo. 9 (1960), 81-120. Math. Rev. 23A, No. 4023.
Pacific Journal of Mathematics
