Determinants and Their Applications in Mathematical Physics

Bibliography 351

U. Elias, Minors of the Wronskian of the differential equationLny+p(x)y=0.

Proc. Roy. Soc. Edin.106A(1987), 341–359. [Zbl 632 (1988), 34027.]

U. Elias, Minors of the Wronskian of the differential equationLny+p(x)y=0.

II. Dominance of solutions.Proc. Roy. Soc. Edin. 108 (1988), 229–239. [Zbl

655 (1989), 34038.]

A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi,Higher Transcendental

Functions, McGraw-Hill, New York, 1953.

F.J. Ernst, Complex potential formulation of the axially symmetric gravitational

field problem.J. Math. Phys. 15 (1974), 1409–1412. [MR 49 (1975), 12028.]

R.J. Evans, I.M. Isaacs, Generalized Vandermonde determinants and roots of

unity of prime order.Proc. Am. Math. Soc. 58 (1976), 51–54. [MR 54 (1977),

332.]

T. Fack, Proof of the conjecture of A. Grothendieck on the Fuglede–Kasidon

determinant.J. Func. Anal. 50 (1983), 215–218. [MR 84m: 46081.]

K. Fan, J. Todd, A determinantal inequality.J. Lond. Math. Soc. 30 (1955),

58–64. [MR 16 (1955), 664.]

D.R. Farenik, P.J. Browne, Gerˇsgorin theory and the definiteness of determinantal

operators.Proc. Roy. Soc. Edin.106A(1987), 1–10. [MR 88m: 47004.]

J. Farges, Solution to Problem 83-11, A nonnegative determinant (Proposed G.N.

Lewis).SIAM Rev. 26 (1984), 431.

C. Farmer, A certain sequence of infinite determinants.J. Math. Anal. Applic.

34 (1971), 228–232. [Zbl 188 (1970), 76.]

A.B. Farnell, A special Vandermondian determinant.Am. Math. Monthly 66

(1959), 564–569. [MR 21 (1960), 6383.]

D. Fearnley-Sander, A characterization of the determinant.Am. Math. Monthly

82 (1975), 838–840. [MR 53 (1977), 2977.]

M. Fiedler, Remarks on the Schur complement.Linear Alg. Applic. 39 (1981),

189–196. [Zbl 465 (1982), 15004.]

M. Fiedler, On a conjecture of P.R. Vein and its generalization.Linear Multilinear

Alg. 16 (1984), 147–154. [Zbl 554 (1985), 15002; MR 86g: 15004.]

H. Filesta, A new method for solving a class of ballot problems.J. Comb. Theory

A 39 (1985), 102–111. [Zbl 579 (1986), 05005.]

N.J. Fine, Solution of Problem 5165 (1964, 99). Alternant type determinant,

proposed by A.S. Galbraith.Am. Math. Monthly 72 (1965), 91–92.

A.M. Fink, Certain determinants related to the Vandermonde.Proc. Am. Math.

Soc. 38 (1973), 483–488. [MR 47 (1974), 239.]

M.E. Fisher, R.E. Hartwig, Toeplitz determinants: Some applications, theorems

and conjectures.Adv. Chem. Phys. 15 (1968), 333–353.

D. Foata, The noncommutative version of the matrix inversion formula.Adv.

Math. 31 (1979), 330–349. [MR 80f: 15006.]

P.J. Forrester, T.D. Hughes, Complex Wishart matrices and conductance in

mesoscopic systems. Exact results.J. Math. Phys. 35 (1994), 6736–6747.

A. Frankel, Solution of Problem 71-2 on Bigradients, proposed by A.S.

Householder.SIAM Rev. 14 (1972), 495–496.