Integral equations associated with Hankel convolutions

Haimo, Deborah Tepper

doi:10.1090/S0002-9947-1965-0185379-4

Integral equations associated with Hankel convolutions
HTML articles powered by AMS MathViewer

by Deborah Tepper Haimo

Trans. Amer. Math. Soc. 116 (1965), 330-375

DOI: https://doi.org/10.1090/S0002-9947-1965-0185379-4

PDF | Request permission

References

Charles Fox, The inversion of convolution transforms by differential operators, Proc. Amer. Math. Soc. 4 (1953), 880–887. MR 58744, DOI 10.1090/S0002-9939-1953-0058744-0
F. R. Gantmacher, Matrizenrechnung. II. Spezielle Fragen und Anwendungen, Hochschulbücher für Mathematik, Band 37, VEB Deutscher Verlag der Wissenschaften, Berlin, 1959 (German). MR 0107647
Richard R. Goldberg, Fourier transforms, Cambridge Tracts in Mathematics and Mathematical Physics, No. 52, Cambridge University Press, New York, 1961. MR 0120501
Deborah Tepper Haimo, Variation diminishing transformations, Bull. Amer. Math. Soc. 70 (1964), 271–274. MR 160083, DOI 10.1090/S0002-9904-1964-11116-2
I. I. Hirschman Jr., Variation diminishing Hankel transforms, J. Analyse Math. 8 (1960/61), 307–336. MR 157197, DOI 10.1007/BF02786854
I. I. Hirschman Jr., Variation diminishing transformations and ultraspherical polynomials, J. Analyse Math. 8 (1960/61), 337–360. MR 157198, DOI 10.1007/BF02786855
I. I. Hirschman Jr., Variation diminishing transformations and orthogonal polynomials, J. Analyse Math. 9 (1961/62), 177–193. MR 133484, DOI 10.1007/BF02795343
I. I. Hirschman Jr., Variation diminishing transformations and Sturm-Liouville systems, Comment. Math. Helv. 36 (1961), 214–233. MR 141817, DOI 10.1007/BF02566900
I. I. Hirschman Jr., Variation-diminishing transformations and general orthogonal polynomials, Canadian J. Math. 16 (1964), 98–107. MR 160082, DOI 10.4153/CJM-1964-010-3
I. I. Hirschman and D. V. Widder, The convolution transform, Princeton University Press, Princeton, N. J., 1955. MR 0073746
I. P. Natanson, Theory of functions of a real variable, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron with the collaboration of Edwin Hewitt. MR 0067952
G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Dover Publications, New York, N.Y., 1945 (German). MR 0015435
I. J. Schoenberg, On totally positive functions, Laplace integrals and entire functions of the Laguerre-Polya-Schur type, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 11–17. MR 18706, DOI 10.1073/pnas.33.1.11
I. J. Schoenberg, On variation-diminishing integral operators of the convolution type, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 164–169. MR 23873, DOI 10.1073/pnas.34.4.164

The theory of functions

Introduction to the theory of Fourier integrals

G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
David V. Widder, Advanced calculus, Prentice Hall Mathematics Series, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1961. 2nd ed. MR 0122921
David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, vol. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923