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Integral equations associated with Hankel convolutions. (English) Zbl 0135.33502


MSC:

45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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References:

[1] Charles Fox, The inversion of convolution transforms by differential operators, Proc. Amer. Math. Soc. 4 (1953), 880 – 887. · Zbl 0052.10902
[2] F. R. Gantmacher, Matrizenrechnung. II. Spezielle Fragen und Anwendungen, Hochschulbücher für Mathematik, Bd. 37, VEB Deutscher Verlag der Wissenschaften, Berlin, 1959 (German). F. R. Gantmacher, Applications of the theory of matrices, Translated by J. L. Brenner, with the assistance of D. W. Bushaw and S. Evanusa, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1959. F. R. Gantmacher, The theory of matrices. Vols. 1, 2, Translated by K. A. Hirsch, Chelsea Publishing Co., New York, 1959.
[3] Richard R. Goldberg, Fourier transforms, Cambridge Tracts in Mathematics and Mathematical Physics, No. 52, Cambridge University Press, New York, 1961. · Zbl 0095.08601
[4] Deborah Tepper Haimo, Variation diminishing transformations, Bull. Amer. Math. Soc. 70 (1964), 271 – 274. · Zbl 0125.34001
[5] I. I. Hirschman Jr., Variation diminishing Hankel transforms, J. Analyse Math. 8 (1960/1961), 307 – 336. · Zbl 0099.31301 · doi:10.1007/BF02786854
[6] I. I. Hirschman Jr., Variation diminishing transformations and ultraspherical polynomials, J. Analyse Math. 8 (1960/1961), 337 – 360. · Zbl 0099.28003 · doi:10.1007/BF02786855
[7] I. I. Hirschman Jr., Variation diminishing transformations and orthogonal polynomials, J. Analyse Math. 9 (1961/1962), 177 – 193. · Zbl 0103.07902 · doi:10.1007/BF02795343
[8] I. I. Hirschman Jr., Variation diminishing transformations and Sturm-Liouville systems, Comment. Math. Helv. 36 (1961), 214 – 233. · Zbl 0109.05804 · doi:10.1007/BF02566900
[9] I. I. Hirschman Jr., Variation-diminishing transformations and general orthogonal polynomials, Canad. J. Math. 16 (1964), 98 – 107. · Zbl 0118.06204 · doi:10.4153/CJM-1964-010-3
[10] I. I. Hirschman and D. V. Widder, The convolution transform, Princeton University Press, Princeton, N. J., 1955. · Zbl 0039.33202
[11] 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. · Zbl 0064.29102
[12] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Dover Publications, New York, N. Y., 1945 (German). · Zbl 0060.12307
[13] 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. · Zbl 0029.36601
[14] I. J. Schoenberg, On variation-diminishing integral operators of the convolution type, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 164 – 169. · Zbl 0036.20301
[15] E. C. Titchmarsh, The theory of functions, 2nd ed., Oxford Univ. Press, Oxford, 1939. · Zbl 0022.14602
[16] -, Introduction to the theory of Fourier integrals, Oxford Univ. Press, Oxford, 1948.
[17] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. · Zbl 0063.08184
[18] David V. Widder, Advanced calculus, 2nd ed. Prentice-Hall Mathematics Series. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1961. · Zbl 0728.26002
[19] David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, v. 6, Princeton University Press, Princeton, N. J., 1941. · Zbl 0063.08245
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