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ЖУРНАЛЫ // Алгебра и анализ

Алгебра и анализ, 2022, том 34, выпуск 3, страницы 51–92 (Mi aa1809)

Stationary phase method, powers of functions, and applications to functional analysis
H. Queffélec, R. Zarouf

Список литературы

1. Agrafeuil C., Zarrabi M., “Closed ideals with countable hull in algebras of analytic functions smooth up to the boundary”, Publ. Mat., 52:1 (2008), 19–56  crossref  mathscinet  zmath
2. Andersson J., Turán's problem $10$ revisited, 2008, arXiv: math/0609271
3. Andersson J., “On some power sum problems of Turán and Erdös”, Acta Math. Hungar., 70:4 (1996), 305–316  crossref  mathscinet  zmath
4. Bayart F., Finet C., Li D., Queffélec H., “Composition operators on the Wiener–Dirichlet algebra”, J. Operator Theory, 60:1 (2008), 45–70  mathscinet  zmath
5. Beurling A., Helson H., “Fourier–Stieltjes transforms with bounded powers”, Math. Scand., 1 (1953), 120–126  crossref  mathscinet  zmath
6. Bleistein N., Handelsman R. A., Asymptotic expansions of integrals, 2nd ed., Dover Publ., Inc., New York, 1986  mathscinet
7. Блюдзе М. Ю., Шиморин С. М., “Оценки норм степеней функций в некоторых банаховых пространствах”, Зап. науч. семин. ПОМИ, 206, 1993, 15–32  mathnet
8. Borichev A., Fouchet K., Zarouf R., On the Fourier coefficients of powers of a Blaschke factor and strongly annular functions, 2021, arXiv: 2107.00405
9. Borovikov V. A., Uniform stationary phase method, IEE Electromagn. Waves Ser., 40, Inst. Engineer. and Technol., London, 1994  mathscinet  zmath
10. de Bruijn N. G., Asymptotic methods in analysis, Bibliotheca Math., IV, North–Holland Publ. Co., Amsterdam, 1958  mathscinet  zmath
11. Chamizo F., Ubis A., “Some Fourier series with gaps”, J. Anal. Math., 101 (2007), 179–197  crossref  mathscinet  zmath
12. Chester C., Friedman B., Ursell F., “An extension of the method of steepest descents”, Proc. Cambridge Philos. Soc., 53 (1957), 599–611  crossref  mathscinet  zmath  adsnasa
13. Cohen P., “Homomorphisms of group algebras”, Amer. J. Math., 82 (1960), 213–226  crossref  mathscinet  zmath
14. Copson E. T., Asymptotic expansions, Cambridge Tracts in Math., 55, Cambridge Univ. Press, New York, 1965  mathscinet  zmath
15. Erdös P., Rényi A., “A probabilistic approach to problems of Diophantine approximation”, Illinois J. Math., 1 (1957), 303–315  crossref  mathscinet  zmath
16. Garnett J., Bounded analytic functions, Pure Appl. Math., 96, Acad. Press, Inc., New York, 1981  mathscinet  zmath
17. Gerver J., “The differentiability of the Riemann function at certain rational multiples of $\pi$”, Amer. J. Math., 92 (1970), 33–55  crossref  mathscinet  zmath
18. Gerver J., “More on the differentiability of the Riemann function”, Amer. J. Math., 93 (1971), 33–41  crossref  mathscinet  zmath
19. Gerver J., “On cubic lacunary Fourier series”, Trans. Amer. Math. Sos., 355:11 (2003), 4297–4337  crossref  mathscinet
20. Girard D. M., “The behavior of the norm of an automorphism of the unit disk”, Pacific J. Math., 47 (1973), 443–456  crossref  mathscinet  zmath
21. Gluskin E., Meyer M., Pajor A., “Zeros of analytic functions and norms of inverse matrices”, Israel J. Math., 87:1-3 (1994), 225–242  crossref  mathscinet  zmath
22. Gordon J., Hedenmalm H., “The composition operators on the space of Dirichlet series with square-summable coefficients”, Michigan Math. J., 46:2 (1999), 313–329  crossref  mathscinet  zmath
23. Graham S., Kolesnik G., van der Corput's method of exponential sums, London Math. Soc. Lecture Notes Ser., 126, Cambridge Univ. Press, Cambridge, 1991  mathscinet
24. Indritz J., “An inequality for Hermite polynomials”, Proc. Amer. Math. Soc., 12 (1961), 981–983  crossref  mathscinet  zmath
25. Itatsu S., “Differentiability of Riemann's function”, Proc. Japan. Acad. Math. Sci., 57:10 (1981), 492–495  mathscinet  zmath
26. Jaffard S., “The spectrum of singularities of Riemann's function”, Rev. Mat. Iberoam., 12:2 (1996), 441–460  crossref  mathscinet  zmath
27. Kahane J.-P., Séries de Fourier absolument convergentes, Ergeb. Math. Grenzgeb., 50, Springer-Verlag, New York, 1970  mathscinet
28. Kahane J.-P., “Sur certaines classes de series de Fourier absolument convergentes”, J. Math. Pure Appl. (9), 35 (1956), 249–259  mathscinet  zmath
29. Lefèvre P., Li D., Queffélec H., Rodríguez-Piazza L., Boundedness of composition operators on general weighted Hardy spaces of analytic functions, 2020, arXiv: 2011.14928  mathscinet
30. Лейбензон З. Л., “О кольце функций с абсолютно сходящимися рядами Фурье”, Успехи мат. наук, 9:3 (1954), 157–162  mathnet  mathscinet
31. Montgomery H. L., Ten lectures on the interface between analytic number theory and harmonic analysis, CBMS Reg. Conf. Ser. Math., 84, Amer. Math. Soc., Providence, RI, 1994  crossref  mathscinet  zmath
32. Newman D., “Homomorphisms of $\ell_{+}$”, American J. Math., 91 (1969), 37–46  crossref  mathscinet  zmath
33. Nikolski N., “Condition numbers of large matrices and analytic capacities”, Алгебра и анализ, 17:4 (2005), 125–180  mathnet  mathscinet
34. Nikolski N., Operators, function, and systems: an easy reading, v. 1, Math. Surveys Monogr., 92, Amer. Math. Soc., Providence, RI, 2002  mathscinet
35. Никольский Н. К., Лекции об операторе сдвига, Наука, М., 1980
36. Queffélec H., Dérivabilité de certaines sommes de séries de Fourier lacunaires, Thèse de troisième cycle, Univ. d'Orsay, 1971  mathscinet
37. Queffélec H., “Dérivabilité de certaines sommes de séries de Fourier lacunaires”, C. R. Acad. Sci. Paris, 273 (1971), 291–293  mathscinet  zmath
38. Queffélec H., “Norm of the inverse of a matrix; solution to a problem of Schäffer”, Harmonic analysis from the pichorides viewpoint (Anogia, 1995), Publ. Math. Orsay, Univ. Paris XI, Orsay, 1996, 68–87  mathscinet  zmath
39. Queffélec H., “Sur un théorème de Gluskin–Meyer–Pajor”, C. R. Acad. Sci. Paris Sér. I Math., 317:2 (1993), 155–158  mathscinet  zmath
40. Queffélec M., Queffélec H., Diophantine approximation and Dirichlet series, Texts and Readings in Math., 80, 2nd ed., Springer, Singapore, 2020  crossref  mathscinet  zmath
41. Robert O., “On van der Corput's $k$th derivative test for exponential sums”, Indag. Math., 27:2 (2016), 559–589  crossref  mathscinet  zmath
42. Rudin W., Fourier analysis on groups, Intersci. Tracts Pure Appl. Math., 12, Intersci. Publ., New York, 1962  mathscinet  zmath
43. Schäffer J. J., “Norms and determinants of linear mappings”, Math. Z., 118 (1970), 331–339  crossref  mathscinet  zmath
44. Shapiro J., Composition operators and classical function theory, Universitext Tracts Math., Springer-Verlag, New-York, 1991  mathscinet
45. Szehr O., Zarouf R., “On the asymptotic behavior of Jacobi polynomials with first varying parameter”, J. Approx. Theory, 277:10 (2022), 105702, 31 pp.  crossref  mathscinet  zmath
46. Szehr O., Zarouf R., “Explicit counterexamples to Schäffer's conjecture”, J. Math. Pures Appl. (9), 146 (2021), 1–30  crossref  mathscinet  zmath
47. Szehr O., Zarouf R., “$l_{p}$-norms of Fourier coefficients of powers of a Blaschke factor”, J. Anal. Math., 140:1 (2020), 1–30  crossref  mathscinet  zmath
48. Szehr O., Zarouf R., A constructive approach to Schäffer conjecture, 2017, arXiv: 1705.10704  zmath
49. Sz.-Nagy B., Foias C., Harmonic analysis of operators on Hilbert space, North-Holland Publ. Co., Amsterdam-London, 1970  mathscinet  zmath
50. Tenenbaum G., Introduction to analytic and probabilistic number theory, Grad. Stud. in Math., 163, Third ed., Amer. Math. Soc., Providence, RI, 2015  crossref  mathscinet  zmath
51. Titchmarsh E. C., The theory of the Riemann zeta function, Second ed., Oxford Univ. Press, New York, 1986  mathscinet  zmath
52. Turán P., On a new method of analysis and its applications, Pure and Appl. Math., Wiley-Intersci. Publ., New-York, 1984  mathscinet  zmath
53. Wong R., Asymptotic approximations of integrals, Classics in Appl. Math., 34, Soc. Industr. Appl. Math. (SIAM), Philadelphia, PA, 2001  mathscinet


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