PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1998 | 130 | 1 | 23-52
Tytuł artykułu

On p-dependent local spectral properties of certain linear differential operators in $L^{p}(ℝ^{N})

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim is to investigate certain spectral properties, such as decomposability, the spectral mapping property and the Lyubich-Matsaev property, for linear differential operators with constant coefficients ( and more general Fourier multiplier operators) acting in $L^p(ℝ^N)$. The criteria developed for such operators are quite general and p-dependent, i.e. they hold for a range of p in an interval about 2 (which is typically not (1,∞)). The main idea is to construct appropriate functional calculi: this is achieved via a combination of methods from the theory of Fourier multipliers and local spectral theory.
Słowa kluczowe
Twórcy
autor
autor
Bibliografia
  • [1] E. Albrecht and R. D. Mehta, Some remarks on local spectral theory, J. Operator Theory 12 (1984), 285-317.
  • [2] E. Albrecht and W. J. Ricker, Local spectral properties of constant coefficient differential operators in $L^p (ℝ^N)$, ibid. 24 (1990), 85-103.
  • [3] E. Albrecht and W. J. Ricker, Functional calculi and decomposability of unbounded multiplier operators in $L^p (ℝ^N)$, Proc. Edinburgh Math. Soc. 38 (1995), 151-166.
  • [4] E. Albrecht and W. J. Ricker, Local spectral properties of certain matrix differential operators in $L^p (ℝ^N)^m$, J. Operator Theory 35 (1996), 3-37.
  • [5] C. Apostol, Spectral decompositions and functional calculus, Rev. Roumaine Math. Pures Appl. 13 (1968), 1481-1528.
  • [6] Y.-C. Chang and P. A. Tomas, Invertibility of some second order differential operators, Studia Math. 79 (1984), 289-296.
  • [7] I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
  • [8] N. Dunford and J. T. Schwartz, Linear Operators I: General Theory, Interscience, New York, 1964.
  • [9] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, Berlin, 1977.
  • [10] C. Foiaş, Spectral maximal spaces and decomposable operators, Arch. Math. (Basel) 14 (1963), 341-349.
  • [11] L. Hörmander, On interior regularity of the solutions of partial differential equations, Comm. Pure Appl. Math. 11 (1958), 197-218.
  • [12] L. Hörmander, Estimates for translation invariant operators in $L^p$ spaces, Acta Math. 104 (1960), 93-140.
  • [13] L. Hörmander, The Analysis of Linear Partial Differential Operators II. Differential Operators with Constant Coefficients, Springer, Berlin, 1983.
  • [14] F. T. Iha and C.F. Schubert, The spectrum of partial differential operators on $L^p(ℝ^n), Trans. Amer. Math. Soc. 152 (1970), 215-226
  • [15] M. Jodeit, Jr., A note on Fourier multipliers, Proc. Amer. Math. Soc. 27 (1971), 423-424.
  • [16] C. E. Kening and P. A. Tomas, On conjectures of Rivière Strichartz, Bull. Amer. Math. Soc. (N.S.) 1 (1979), 694-697).
  • [17] C. E. Kening and P. A. Tomas, $L^p$ behaviour of certain second order partial differential operators, Trans. Amer. Math. Soc. 262 (1980), 521-531.
  • [18] H. König and R. Reader, Vorlesung über die Theorie der Distributionen, Ann. Univ. Sarav. Ser. Math. 6 (1995), 1-213.
  • [19] K. de Leeuw, On $L^p$ multipliers, Ann. of Math. 81 (1965), 364-379.
  • [20] W. Littman, Multipliers in $L^p$ and interpolation, Bull. Amer. Math. Soc. 71 (1965), 764-766.
  • [21] Yu. I. Lyubich and V. I. Matsaev, On operators with separable spectrum, Mat. Sb. 56 (1962), 433-468.
  • [22] J. Peetre, Applications de la théorie des espaces d'interpolation dans l'Analyse Harmonique, Ricerche Mat. 15 (1966), 3-36.
  • [23] A. Ruiz, Multiplicadores asociados a curvas en el plano y teoremas de restricción de la transformada de Fourier a curvas en $ℝ ^2$ y ℝ ^3$, Tesis doctoral, Universidad Complutense de Madrid, 1980.
  • [24] A. Ruiz, $L^p$ - boundedness of a certain class of multipliers associated with curves on the plane. I, Proc. Amer. Math. Soc. 87 (1983), 271-276.
  • [25] A. Ruiz, $L^p$ - boundedness of a certain class of multipliers associated with curves on the plane. II, ibid., 277-282.
  • [26] M. Schechter, The spectrum of operators on $L^p (E^n)$, Ann. Scoula Norm. Sup. Pisa 24 (1970), 201-207.
  • [27] M. Schechter, Spectra of Partial Differential Operators, 2nd ed., North-Holland, Amsterdam, 1986.
  • [28] F.-H. Vasilescu, Analytic Functional Calculus and Spectral Decompositions, D. Reidel, Dordrecht, and Editura Academiei, Bucureşti, 1982.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv130i1p23bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.