Selected Publications

Academic Article

Year Title Altmetric
2021 Inequalities of Rellich TypeFunctional Analysis and Its Applications.  55:130-139. 2021
2012 A geometric characterization of a sharp Hardy inequalityJournal of Functional Analysis.  262:3159-3185. 2012
2012 Hardy's inequality and curvatureJournal of Functional Analysis.  262:648-666. 2012
2008 On inequalities of hardy-sobolev typeBanach Journal of Mathematical Analysis.  2:94-106. 2008
2005 Counting eigenvalues of biharmonic operators with magnetic fields 2005
2005 On the Rellich inequality with magnetic potentialsMathematische Zeitschrift.  251:267-284. 2005
2001 On the number of negative eigenvalues of Schrödinger operators with an Aharonov-Bohm magnetic fieldProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.  457:2481-2489. 2001
2001 Sobolev, Hardy and CLR inequalities associated with Pauli operators in ℝ 3Journal of Physics A: Mathematical and Theoretical.  34. 2001
1999 Eigenvalue estimates in the semi-classical limit for Pauli and Dirac operators with a magnetic fieldProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.  455:183-217. 1999
1996 Counting eigenvalues using coherent states with an application to dirac and schrödinger operators in the semi-classical limit 1996
1993 On the number of bound states of a bosonic N-particle Coulomb systemMathematische Zeitschrift.  214:441-459. 1993
1992 Zhislin's theorem revisited 1992
1991 Some geometric spectral properties of N-body Schrödinger operatorsArchive for Rational Mechanics and Analysis.  113:377-400. 1991
1990 N-bodys chrÖdinger operators with finitely many bound statesTransactions of the American Mathematical Society.  322:593-626. 1990
1986 Eigenvalues below the essential spectra of singular elliptic operatorsTransactions of the American Mathematical Society.  297:197-222. 1986
1984 A Friedrichs inequality and an application 1984
1982 Singular elliptic operators of second order with purely discrete spectraTransactions of the American Mathematical Society.  271:653-666. 1982
1981 The effect of variable change on oscillation and disconjugacy criteria with applications to spectral theory and asymptotic theoryJournal of Mathematical Analysis and Applications.  81:234-277. 1981
1981 The spectra of some singular elliptic operators of second orderNorth Holland Mathematics Studies.  55:303-318. 1981
1981 Transformations of ordinary differential operatorsNorth Holland Mathematics Studies.  55:1-7. 1981
1980 Comparison and oscillation criteria for selfadjoint vector-matrix differential equationsPacific Journal of Mathematics.  90:125-134. 1980
1980 Oscillation theory for generalized second-order differential equationsRocky Mountain Journal of Mathematics.  10:751-766. 1980
1980 The Oscillation of Elliptic Systems 1980
1979 Positive functionals and oscillation criteria for second order differential systemsProceedings of the Edinburgh Mathematical Society.  22:277-290. 1979
1978 Oscillation theory at a finite singularityJournal of Differential Equations.  30:235-247. 1978
1978 Spectral analysis of second order difference equationsJournal of Mathematical Analysis and Applications.  63:421-438. 1978
1977 Conjugate points of vector-matrix differential equationsTransactions of the American Mathematical Society.  231:167-178. 1977
1976 The existence of conjugate points for selfadjoint differential equations of even orderProceedings of the American Mathematical Society.  56:162-166. 1976
1974 Oscillation and nonoscillation criteria for some self-adjoint even order linear differential operatorsPacific Journal of Mathematics.  51:221-234. 1974
1974 The discreteness of the spectrum of selfadjoint, even order, one-term, differential operatorsProceedings of the American Mathematical Society.  42:480-482. 1974


Year Title Altmetric
1984 Preface.  Ed. 92.  1984
1981 Preface.  Ed. 55.  1981

Education And Training

  • Doctor of Philosophy in Mathematics, University of Tennessee System : Knoxville 1972
  • Full Name

  • Roger Lewis