Bibliography for the Maximum Modulus Principle

short

 

  1. Distance between a Maximum Modulus Point and Zero Set of an Entire Function
    Ostrovskii I.; Ersin Ureyen A.
    Complex Variables, July 2003, vol. 48, no. 7, pp. 583-598(16), Ingenta.
  2. Finding the maximum modulus roots of polynomials based on constrained neural networks
    Huang, De-Shuang; Ip, Horace H.S.
    ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, v 2, 2003, p 797-800, Compendex.  
  3. On the maximum modulus of weighted polynomials in the plane, a theorem of  Rakhmanov, Mhaskar and Saff revisited
    Damelin S.B.
    Journal of Computational and Applied Mathematics, 15 June 2003, vol. 155, no. 2, pp. 455-459(5), Ingenta.
  4. Weak pseudoconcavity and the maximum modulus principle.
    Hill, C. Denson; Nacinovich, Mauro
    Ann. Mat. Pura Appl. (4) 182 (2003), no. 1, 103--112, MathSciNet.  
  5. On Influence of the Arguments of Coefficients of a Power Series Expansion of an Entire Function on the Growth of the Maximum of Its Modulus
    Filevich P.V.
    Siberian Mathematical Journal, May 2003, vol. 44, no. 3, pp. 529-538(10), Ingenta.
  6. On the Maximum of the Modulus and the Maximal Term of Dirichlet Series
    Sheremeta M.N.
    Mathematical Notes, March 2003, vol. 73, no. 3-4, pp. 402-407(6), Ingenta.
  7. Best Constants in the Miranda-Agmon Inequalities for Solutions of Elliptic Systems and the Classical Maximum Modulus Principle for Fluid and Elastic Half-spaces
    Kresin G.I.; Maz'ya V.G.
    Applicable Analysis, 2003, vol. 82, no. 2, pp. 157-185(29), Ingenta.
  8. On the Growth of the Maximum of the Modulus of an Entire Function on a Sequence
    Filevych P.V.
    Ukrainian Mathematical Journal, August 2002, vol. 54, no. 8, pp. 1386-1392(7), Ingenta.
  9. The generalization of maximum modulus principle. (Chinese)
    Li, Yun Xia
    Math. Practice Theory 30 (2000), no. 2, 153--155, MathSciNet.  
  10. Criteria for validity of the maximum modulus and the maximum norm principles for solutions of linear parabolic systems.
    Maz'ya, Vladimir
    Complex analysis and differential equations (Uppsala, 1997), 249--254, Acta Univ. Upsaliensis Skr. Uppsala Univ. C Organ. Hist., 64, Uppsala Univ., Uppsala, 1999, MathSciNet.  
  11. On the maximum modulus of polynomials
    Dewan, K.K.; Kaur, Jagjeet
    Journal of Mathematical Analysis and Applications, v 181, n 2, Jan 15, 1994, p 493, Compendex.  
  12. Liouville's theorem and the maximum modulus principle for a system of complex vector fields.
    Berhanu, S.
    Comm. Partial Differential Equations 19 (1994), no. 11-12, 1805--1827, MathSciNet.  
  13. Derivatives of the maximum modulus of a starlike function
    London, R.R.
    Analysis Mathematica, v 19, n 1, 1993, p 39, Compendex.  
  14. Criteria for validity of the maximum modulus principle for solutions of linear strongly elliptic second order systems.
    Kresin, Gregory I.; Maz'ya, Vladimir G.
    Potential Anal. 2 (1993), no. 1, 73--99, MathSciNet.  
  15. On the Maximum Modulus of Polynomials
    M. A. Qazi
    Proceedings of the American Mathematical Society, Vol. 115, No. 2 (Jun., 1992), pp. 337-343, Jstor.  
  16. Maximum modulus sets in pseudoconvex boundaries
    Iordan, Andrei
    Journal of Geometric Analysis, v 2, n 4, 1992, p 327, Compendex.  
  17. Integrals with a large parameter and the maximum-modulus principle.
    Ursell, F.
    Asymptotic and computational analysis (Winnipeg, MB, 1989), 477--489, Lecture Notes in Pure and Appl. Math., 124, Dekker, New York, 1990, MathSciNet.  
  18. On the maximum modulus principle for solutions of linear parabolic systems.
    Kresin, G. I.; Maz'ya, V. G.
    Seminar Analysis (Berlin, 1988/1989), 41--50, Akad. Wiss. DDR, Berlin, 1989, MathSciNet.  
  19. Some boundary properties of bounded analytic functions and the maximum modulus principle in arbitrarily connected domains. (Russian)
    Samokhin, M. V.
    Mat. Sb. (N.S.) 135(177) (1988), no. 4, 497--513, 559--560; translation in Math. USSR-Sb. 63 (1989), no. 2, 483--498, MathSciNet.  
  20. Maximum modulus theorem for linear fractional transformations
    Packard, Andy; Balsamo, J. Whitney
    Systems & Control Letters, v 11, n 5, Nov, 1988, p 365-367, Compendex.  
  21. Maximum modulus principle and rings of continuous complex functions.
    Khan, Abdul Rauf
    Proc. Pakistan Acad. Sci. 24 (1987), no. 2, 161--167, MathSciNet.  
  22. The maximum principle for the modulus and gradient of a solution for quasilinear elliptic equations. (Russian)
    Baizaev, S.
    Dokl. Akad. Nauk Tadzhik. SSR 27 (1984), no. 9, 481--484, MathSciNet.  
  23. The maximum modulus principle in the algebra R(X). (Spanish)
    Valdés Castro, Concepción
    Cienc. Mat. (Havana) 2 (1981), no. 1, 110--116, MathSciNet.  
  24. A direct proof of the fact that L1 X,B,µ satisfies the strong maximum modulus principle. (Romanian)
    Anghel, Nicolae
    Bul. Inst. Politehn. Bucuresti Ser. Electrotehn. 42 (1980), no. 1, 15--19, MathSciNet.  
  25. Application of L. S. Pontrjagin's maximum principle to the solution of extremal problems in a class of functions with bounded mean modulus. (Russian)
    Vazdaev, V. P.
    Sibirsk. Mat. Zh. 21 (1980), no. 3, 42--55, 235, MathSciNet.  
  26. The maximum modulus principle. I. Necessary conditions.
    Ellis, David; Hill, C. Denson; Seabury, Chester C.
    Indiana Univ. Math. J. 25 (1976), no. 7, 709--715, MathSciNet.  
  27. Pseudoconvexity and the principle of maximum modulus.
    Fadlalla, A. A.
    Complex analysis and its applications (Lectures, Internat. Sem., Trieste, 1975), Vol. II, pp. 209--212. Internat. Atomic Energy Agency, Vienna, 1976, MathSciNet.  
  28. The local maximum modulus principle for function spaces.
    Hirashita, Yukio; Wada, Junzo
    Proc. Japan Acad. 51 (1975), 109--112, MathSciNet.  
  29. Theorem on Maximum Modulus
    Anatole Beck
    Proceedings of the American Mathematical Society, Vol. 15, No. 3 (Jun., 1964), pp. 345-349, Jstor.    
  30. The Local Maximum Modulus Principle
    Hugo Rossi
    The Annals of Mathematics, 2nd Ser., Vol. 72, No. 1 (Jul., 1960), pp. 1-11, Jstor.    
  31. On the Maximum Modulus of Polynomials
    T. J. Rivlin
    The American Mathematical Monthly, Vol. 67, No. 3 (Mar., 1960), pp. 251-253, Jstor.   
  32. A Maximum Modulus Property of Maximal Subalgebras
    Paul Civin
    Proceedings of the American Mathematical Society, Vol. 10, No. 1 (Feb., 1959), pp. 51-54, Jstor.  
  33. The Maximum Modulus Principle for CR Functions
    Andrei Iordan
    Proceedings of the American Mathematical Society, Vol. 96, No. 3 (Mar., 1986), pp. 465-469, Jstor.   
  34. The maximum modulus principle for CR functions on smooth real embedded submanifolds of Cn.
    Ellis, David; Hill, C. Denson
    Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 1, Williams Coll., Williamstown, Mass., 1975), pp. 139--140. Amer. Math. Soc., Providence, R. I., 1977, MathSciNet.  
  35. On the maximum modulus principle for the tangential Cauchy-Riemann equations.
    Carlson, James A.; Hill, C. Denson
    Math. Ann. 208 (1974), 91--97, MathSciNet.  
  36. A Maximum Modulus Principle for Closed Algebras of Lipschitz Functions  
    R. M. Crownover
    The American Mathematical Monthly, Vol. 76, No. 9 (Nov., 1969), pp. 1039-1040, Jstor.  
  37. A Curvilinear Extension of the Maximum Modulus Principle
    Frederick Bagemihl
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 63, No. 1 (May, 1969), pp. 36-37, Jstor.  
  38. Maximum Modulus of Some Expressions of Limited Analytic Functions
    Soichi Kakeya
    Transactions of the American Mathematical Society, Vol. 22, No. 4 (Oct., 1921), pp. 489-504, Jstor.  
  39. On the Maximum Modulus of an Analytic Function
    T. H. Gronwall
    The Annals of Mathematics, 2nd Ser., Vol. 16, No. 1/4 (1914), pp. 77-81, Jstor.  
  40. Calculating the Maximum Modulus of a Polynomial Using Steckin's Lemma
    J. J. Green
    SIAM Journal on Numerical Analysis, Vol. 36, No. 4 (May, 1999), pp. 1022-1029, Jstor.  
  41. A Strong Maximum Modulus Theorem For Maximal Function Algebras
    H. S. Bear
    Transactions of the American Mathematical Society, Vol. 92, No. 3 (Sep., 1959), pp. 465-469, Jstor.  
  42. The Strong Maximum Modulus Theorem for Analytic Functions into a Banach Space
    Edward Thorp; Robert Whitley
    Proceedings of the American Mathematical Society, Vol. 18, No. 4 (Aug., 1967), pp. 640-646, Jstor.  
  43. Maximum Modulus Convexity and the Location of Zeros of an Entire Function
    Faruk F. Abi-Khuzam
    Proceedings of the American Mathematical Society, Vol. 106, No. 4 (Aug., 1989), pp. 1063-1068, Jstor.   
  44. On Maximum and Minimum Values of the Modulus of a Polynomial
    D. N. Lehmer
    The Annals of Mathematics, 2nd Ser., Vol. 8, No. 4 (Jul., 1907), pp. 175-176, Jstor.   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2006