Sturm-Liouville theory
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1: Bibliography E
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A catalogue of Sturm-Liouville differential equations.
In Sturm-Liouville theory,
pp. 271–331.
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Charles Sturm and the development of Sturm-Liouville theory in the years 1900 to 1950.
In Sturm-Liouville theory,
pp. 45–74.
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2: 1.13 Differential Equations
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§1.13(viii) Eigenvalues and Eigenfunctions: Sturm-Liouville and Liouville forms
…3: Bibliography
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Sturm-Liouville Theory.
Birkhäuser Verlag, Basel.
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4: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►The materials developed here follow from the extensions of the Sturm–Liouville theory of second order ODEs as developed by Weyl, to include the limit point and limit circle singular cases.
…Friedman (1990) provides a useful introduction to both approaches; as does the conference proceeding Amrein et al. (2005), overviewing the combination of Sturm–Liouville theory and Hilbert space theory.
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5: Bibliography S
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Sturm oscillation and comparison theorems.
In Sturm-Liouville theory,
pp. 29–43.
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6: Errata
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►The spectral theory of these operators, based on Sturm-Liouville and Liouville normal forms, distribution theory, is now discussed more completely, including linear algebra, matrices, matrices as linear operators, orthonormal expansions, Stieltjes integrals/measures, generating functions.
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7: 18.38 Mathematical Applications
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Approximation Theory
… ►The basic ideas of Gaussian quadrature, and their extensions to non-classical weight functions, and the computation of the corresponding quadrature abscissas and weights, have led to discrete variable representations, or DVRs, of Sturm–Liouville and other differential operators. … ►Complex Function Theory
… ►Random Matrix Theory
… ►Coding Theory
…8: Bibliography M
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The Theory of Groups.
Clarendon Press, Oxford.
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Zur Theorie des zylindrisch-parabolischen Spiegels.
Z. Physik 118, pp. 343–356 (German).
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Loud Speakers: Theory, Performance, Testing and Design.
Oxford University Press, New York.
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Singular integrals whose kernels involve certain Sturm-Liouville functions. I.
J. Math. Mech. 19 (10), pp. 855–873.
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Higher monotonicity properties of certain Sturm-Liouville functions. V.
Proc. Roy. Soc. Edinburgh Sect. A 77 (1-2), pp. 23–37.
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9: Bibliography L
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Essai sur la Théorie des Nombres.
2nd edition, Courcier, Paris.
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Zur Theorie der Gaußschen Summen.
Math. Ann. 57 (4), pp. 554–567 (German).
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Higher monotonicity properties of certain Sturm-Liouville functions. III.
Canad. J. Math. 22, pp. 1238–1265.
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Higher monotonicity properties of certain Sturm-Liouville functions. IV.
Canad. J. Math. 24, pp. 349–368.
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Higher monotonicity properties of certain Sturm-Liouville functions..
Acta Math. 109, pp. 55–73.
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10: Bibliography B
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Random and Restricted Walks: Theory and Applications.
Gordon and Breach, New York.
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Uniform approximation: A new concept in wave theory.
Science Progress (Oxford) 57, pp. 43–64.
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Efficiency and Security of Cryptosystems Based on Number Theory.
Ph.D. Thesis, Swiss Federal Institute of Technology (ETH), Zurich.
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Über Sturm-Liouvillesche Polynomsysteme.
Math. Z. 29 (1), pp. 730–736.
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A Sturm-Liouville eigenproblem of the fourth kind: A critical latitude with equatorial trapping.
Stud. Appl. Math. 101 (4), pp. 433–455.
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