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By Lucia M., Magtone R., Zhou H.-S.
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Extra resources for A dirichlet problem with asymptotically linear and changing sign nonlinearity
103 (1977), no. 1, 69-111 (Russian); English transl, in Math. USSR Sb. 32 (1977). 10. Ra~evskii P. , Closed ideals in a countably-normed algebra of entire analytic functions, Dokl. Akad. Nauk SSSR 162 (1965), 513-515 (Russian); English transl, in Soviet Math. Dokl. 6 (1965), 717. 11. KrasiSkov I. , Closed ideals in locallyconvex algebras of entire functions. I, II, Izv. Akad. Nauk SSSR, ser. matem. 31 (1967), 37-60 (Russian); English transl, in Math. USSR Izvestija 81 (1967), 35-55; Izv. Akad. Nauk SSSR, set.
3, 320-330. (Russian) 8. Mergeljan S. , On completeness of a system of analytic functions, Uspekhi Matem. Nauk 8 (1953), no. 4, 3-63. (Russian) 9. , Shapiro H. , Shields A. , Weakly invertible elements in the space of squaresummable holomorphic functions, J. London Math. Soc. 9 (1974), 183-192. 10. Shields A. , Weighted shift operators and analytic function theory, Topics in Operator Theory, Amer. Math. , Providence, R. , 1974, pp. 49-128. 11. , Invariant subspaees and weighted polynomial approximation, Ark.
E. At vanishing on the zero set of the ideal I the following inclusion F M E I holds? PROBLEM 2. e. for any F in A r such that, for any x E C n, the g e r m os F at x is in the integral closure o / t h e ideal Iz in 0 ~ , does one have F inf(n'm) E I (or at least F ~ E I, w i t h s o m e e x p o n e n t t~ depending only on n)? PROBLEM 3. W h e n m << n and the zero set of I is n - m dimensional, is the ideal I d o s e d in air ? A positive answer to these three questions (with ~ = 2 inf(m + 1, n)) is given in  in the very particular case where r a n k F -- 1.
A dirichlet problem with asymptotically linear and changing sign nonlinearity by Lucia M., Magtone R., Zhou H.-S.