Generalized Faber expansions of hyperfunctions on analytic curves

Ahmed I. ZAYED

doi:10.2969/jmsj/04210155

Ahmed I. ZAYED

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 1 Pages 155-170

DOI https://doi.org/10.2969/jmsj/04210155

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Published: 1990 Received: February 24, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Dienes, The Taylor Series, Dover, New York, 1957.
2) G. Faber, Uber polynomische Entwicklungen, Math. Ann., 57 (1903), 389-408.
3) I. Gelfand and G. Silov, Generalized Functions, Vol. I, II, Academic Press, New York, 1964, 1968.
4) I. Gelfand and G. Silov, Quelques applications de la theorie des fonctions genéralisées, J. Math. Pures Appl., 35 (1956), 383-413.
5) R. Gilbert, Function Theoretic Methods in Partial Differential Equations, Academic Press, New York, 1969.
6) A. Grothendieck, Sur certains espaces de fonctions holomorphes, J. Reine Angew. Math., 192 (1953), 35-64, 77-95.
7) L. Iliev, Series of Faber polynomials, the coefficients of which have a finite number of values, Dokl. Akad. Nauk SSSR, 40 (1953), 499-502.
8) G. Johnson, Harmonic functions on the unit disc 1, Illinois J. Math., 12 (1968), 366-385.
9) B. Khavin, Analytic continuation of power series and Faber polynomials, Dokl. Akad. Nauk SSSR, 118 (1958), 879-881.
10) G. Köthe, Topological Vector Spaces, I, II, Springer Verlag, 1969.
11) G. Köthe, Dualität in der Funktionentheorie, J. Reine. Angew. Math., 191 (1953), 30-49.
12) G. Köthe, Die Randverteilungen analytischer Funktionen, Math. Z., 57 (1952), 13-33.
13) J. Lions and E. Magenes, Problèms aux limites non homogènes (VII), Ann. Mat. Pura Appl., 63 (1963), 201-224.
14) A. Martineau, Les hyperfonctions de M. Sato, Sèminaire Bourbaki, 1960/1961, 214, Benjamin, New York, Amsterdam, 1966.
15) C. Roumieu, Sur quelques extensions de la notion de distribution, Ann. Sci. École Norm. Sup., 77 (1960), 41-121.
16) M. Sato, The theory of hyperfunctions, Sûgaku, 10 (1958), 1-27.
17) M. Sato, Theory of hyperfunctions I, II, J. Fac. Sci. Univ. Tokyo, 8 (1959),139-193, 387-437.
18) M. Sato, T. Kawai and M. Kashiwara, Microfunctions and Pseudo differential equations, in Hyperfunctions and Pseudo Differential Equations, Lecture Notes in Math., 287, Springer Verlag, 1971.
19) L. Schwartz, Théorie des distributions, Actualités Sci. Indust., 1245 (1957) and 1122 (1957).
20) V. Smirnov and N. Lebedev, Functions of a Complex Variable, MIT Press, Cambridge, 1968.
21) P. Suetin, Fundamental properties of Faber polynomials, Russian Math. Surveys, 19 (1964), 121-149.
22) G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., 23(1978).
23) E. Titchmarsh, The Theory of Functions, Oxford Univ. Press, Oxford, England, 1932.
24) A. Zayed, M. Freund and E. Görlich, A theorem of Nehari revisited, J. of Complex variables, theory and applications, 10 (1988), 11-22.
25) A. Zayed and G. Walter, Series of orthogonal polynomials as hyperfunctions, SIAM. J. Math, Anal., 13 (1982), 664-675.
26) A. Zayed. Hyperfunctions as boundary values of generalized axiall symmetric potentials, Illinois J. Math., 25 (1981), 306-317.

Right : [1] P. Dienes, The Taylor Series, Dover, New York, 1957.
[2] G. Faber, Uber polynomische Entwicklungen, Math. Ann., 57 (1903), 389-408.
[3] I. Gelfand and G. Silov, Generalized Functions, Vol. I, II, Academic Press, New York, 1964, 1968.
[4] I. Gelfand and G. Silov, Quelques applications de la theorie des fonctions genéralisées, J. Math. Pures Appl., 35 (1956), 383-413.
[5] R. Gilbert, Function Theoretic Methods in Partial Differential Equations, Academic Press, New York, 1969.
[6] A. Grothendieck, Sur certains espaces de fonctions holomorphes, J. Reine Angew. Math., 192 (1953), 35-64, 77-95.
[7] L. Iliev, Series of Faber polynomials, the coefficients of which have a finite number of values, Dokl. Akad. Nauk SSSR, 40 (1953), 499-502.
[8] G. Johnson, Harmonic functions on the unit disc 1, Illinois J. Math., 12 (1968), 366-385.
[9] B. Khavin, Analytic continuation of power series and Faber polynomials, Dokl. Akad. Nauk SSSR, 118 (1958), 879-881.
[10] G. Köthe, Topological Vector Spaces, I, II, Springer Verlag, 1969.
[11] G. Köthe, Dualität in der Funktionentheorie, J. Reine. Angew. Math., 191 (1953), 30-49.
[12] G. Köthe, Die Randverteilungen analytischer Funktionen, Math. Z., 57 (1952), 13-33.
[13] J. Lions and E. Magenes, Problèms aux limites non homogènes (VII), Ann. Mat. Pura Appl., 63 (1963), 201-224.
[14] A. Martineau, Les hyperfonctions de M. Sato, Séminaire Bourbaki, 1960/1961, 214, Benjamin, New York, Amsterdam, 1966.
[15] C. Roumieu, Sur quelques extensions de la notion de distribution, Ann. Sci. École Norm. Sup., 77 (1960), 41-121.
[16] M. Sato, The theory of hyperfunctions, Sûgaku, 10 (1958), 1-27.
[17] M. Sato, Theory of hyperfunctions I, II, J. Fac. Sci. Univ. Tokyo, 8 (1959), 139-193, 387-437.
[18] M. Sato, T. Kawai and M. Kashiwara, Microfunctions and Pseudo differential equations, in Hyperfunctions and Pseudo Differential Equations, Lecture Notes in Math., 287, Springer Verlag, 1971.
[19] L. Schwartz, Théorie des distributions, Actualités Sci. Indust., 1245 (1957) and 1122 (1957).
[20] V. Smirnov and N. Lebedev, Functions of a Complex Variable, MIT Press, Cambridge, 1968.
[21] P. Suetin, Fundamental properties of Faber polynomials, Russian Math. Surveys, 19 (1964), 121-149.
[22] G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., 23 (1978).
[23] E. Titchmarsh, The Theory of Functions, Oxford Univ. Press, Oxford, England, 1932.
[24] A. Zayed, M. Freund and E. Görlich, A theorem of Nehari revisited, J. of Complex variables, theory and applications, 10 (1988), 11-22.
[25] A. Zayed and G. Walter, Series of orthogonal polynomials as hyperfunctions, SIAM. J. Math, Anal., 13 (1982), 664-675.
[26] A. Zayed. Hyperfunctions as boundary values of generalized axiall symmetric potentials, Illinois J. Math., 25 (1981), 306-317.

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