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Classical operators on the Hörmander algebras
1. | Facultad de Magisterio, Universitat de València, Avda. Tarongers, 4, E-46022-Valencia, Spain |
2. | Instituto Universitario de Matemática Pura y Aplicada, IUMPA Universitat Politència, Camino de Vera, s/n., E-46022 Valencia, Spain |
3. | Departamento de Análisis Matemático, Universitat de València, C/ Dr. Moliner, 50, E-46100-Burjassot, Spain |
References:
[1] |
A. Albanese, J. Bonet and W. J. Ricker, Mean ergodic operators in Fréchet spaces, Ann. Acad. Sci. Fenn. Math., 34 (2009), 401-436. |
[2] |
A. Albanese, J. Bonet and W. J. Ricker, On mean ergodic operators, Oper. Theory Adv. Appl., 201 (2010), 1-20. |
[3] |
F. Bayart and E. Matheron, Dynamics of Linear Operators, Cambridge Tracts in Mathematics 179, Cambridge University Press, Cambridge, 2009.
doi: 10.1017/CBO9780511581113. |
[4] |
M. J. Beltrán, Dynamics of differentiation and integration operators on weighted spaces of entire functions, Studia Math., 221 (2014), 35-60.
doi: 10.4064/sm221-1-3. |
[5] |
M. J. Beltrán, J. Bonet and C. Fernández, Classical operators on weighted Banach spaces of entire functions, Proc. Amer. Math. Soc., 141 (2013), 4293-4303.
doi: 10.1090/S0002-9939-2013-11685-0. |
[6] |
C. Berenstein and R. Gay, Complex Analysis and Special Topics in Harmonic Analysis, Springer, New York, 1995.
doi: 10.1007/978-1-4613-8445-8. |
[7] |
C. Berenstein and B. A. Taylor, A new look at interpolation theory for entire functions of one variable, Adv. in Math., 33 (1979), 109-143.
doi: 10.1016/S0001-8708(79)80002-X. |
[8] |
L. Bernal-González and A. Bonilla, Exponential type of hypercyclic entire functions, Arch. Math. (Basel), 78 (2002), 283-290.
doi: 10.1007/s00013-002-8248-7. |
[9] |
K. D. Bierstedt, J. Bonet and J. Taskinen, Associated weights and spaces of holomorphic functions, Stud. Math., 127 (1998), 137-168. |
[10] |
K. D. Bierstedt, R. Meise and W. H. Summers, A projective description of weighted inductive limits, Trans. Am. Math. Soc., 272 (1982), 107-160.
doi: 10.1090/S0002-9947-1982-0656483-9. |
[11] |
K. D. Bierstedt and W. H. Summers, Biduals of weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A, 54 (1993), 70-79.
doi: 10.1017/S1446788700036983. |
[12] |
C. Blair and L. A. Rubel, A triply universal entire function, Enseign. Math. (2), 30 (1984), 269-274. |
[13] |
J. Bonet, Hypercyclic and chaotic convolution operators, J. London Math. Soc., 62 (2000), 253-262.
doi: 10.1112/S0024610700001174. |
[14] |
J. Bonet, Dynamics of the differentiation operator on weighted spaces of entire functions, Math. Z., 261 (2009), 649-677.
doi: 10.1007/s00209-008-0347-0. |
[15] |
J. Bonet and A. Bonilla, Chaos of the differentiation operator on weighted Banach spaces of entire functions, Complex Anal. Oper. Theory, 7 (2013), 33-42.
doi: 10.1007/s11785-011-0134-5. |
[16] |
R. Braun, Weighted algebras of entire functions in which each closed ideal admits two algebraic generators, Michigan Math. J., 34 (1987), 441-450.
doi: 10.1307/mmj/1029003623. |
[17] |
K. G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math., 139 (2000), 47-68. |
[18] |
K. G. Grosse-Erdmann and A. Peris, Linear Chaos, Springer, London, 2011.
doi: 10.1007/978-1-4471-2170-1. |
[19] |
A. Harutyunyan and W. Lusky, On the boundedness of the differentiation operator between weighted spaces of holomorphic functions, Studia Math., 184 (2008), 233-247.
doi: 10.4064/sm184-3-3. |
[20] |
W. Lusky, On the Fourier series of unbounded harmonic functions, J. London Math. Soc., 61 (2000), 568-580.
doi: 10.1112/S0024610799008443. |
[21] |
F. Martínez-Giménez and A. Peris, Chaos for backward shift operators, Int. J. Bifurcation and Chaos, 12 (2002), 1703-1715.
doi: 10.1142/S0218127402005418. |
[22] |
G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal., 98 (1991), 229-269.
doi: 10.1016/0022-1236(91)90078-J. |
[23] |
R. Meise, Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals, J. Reine Angew. Math., 363 (1985), 59-95.
doi: 10.1515/crll.1985.363.59. |
[24] |
R. Meise and B. A. Taylor, Sequence space representations for (FN)-algebras of entire functions modulo closed ideals, Studia Math., 85 (1987), 203-227. |
[25] |
R. Meise and D. Vogt, Introduction to Functional Analysis, The Clarendon Press, Oxford University Press, New York, 1997. |
[26] |
H. Neus, Über die Regularitätsbegriffe induktiver lokalkonvexer Sequenzen, Manuscripta Math., 25 (1978), 135-145.
doi: 10.1007/BF01168605. |
[27] |
E. Wolf, Weighted Fréchet spaces of holomorphic functions, Stud. Math., 174 (2006), 255-275.
doi: 10.4064/sm174-3-3. |
show all references
References:
[1] |
A. Albanese, J. Bonet and W. J. Ricker, Mean ergodic operators in Fréchet spaces, Ann. Acad. Sci. Fenn. Math., 34 (2009), 401-436. |
[2] |
A. Albanese, J. Bonet and W. J. Ricker, On mean ergodic operators, Oper. Theory Adv. Appl., 201 (2010), 1-20. |
[3] |
F. Bayart and E. Matheron, Dynamics of Linear Operators, Cambridge Tracts in Mathematics 179, Cambridge University Press, Cambridge, 2009.
doi: 10.1017/CBO9780511581113. |
[4] |
M. J. Beltrán, Dynamics of differentiation and integration operators on weighted spaces of entire functions, Studia Math., 221 (2014), 35-60.
doi: 10.4064/sm221-1-3. |
[5] |
M. J. Beltrán, J. Bonet and C. Fernández, Classical operators on weighted Banach spaces of entire functions, Proc. Amer. Math. Soc., 141 (2013), 4293-4303.
doi: 10.1090/S0002-9939-2013-11685-0. |
[6] |
C. Berenstein and R. Gay, Complex Analysis and Special Topics in Harmonic Analysis, Springer, New York, 1995.
doi: 10.1007/978-1-4613-8445-8. |
[7] |
C. Berenstein and B. A. Taylor, A new look at interpolation theory for entire functions of one variable, Adv. in Math., 33 (1979), 109-143.
doi: 10.1016/S0001-8708(79)80002-X. |
[8] |
L. Bernal-González and A. Bonilla, Exponential type of hypercyclic entire functions, Arch. Math. (Basel), 78 (2002), 283-290.
doi: 10.1007/s00013-002-8248-7. |
[9] |
K. D. Bierstedt, J. Bonet and J. Taskinen, Associated weights and spaces of holomorphic functions, Stud. Math., 127 (1998), 137-168. |
[10] |
K. D. Bierstedt, R. Meise and W. H. Summers, A projective description of weighted inductive limits, Trans. Am. Math. Soc., 272 (1982), 107-160.
doi: 10.1090/S0002-9947-1982-0656483-9. |
[11] |
K. D. Bierstedt and W. H. Summers, Biduals of weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A, 54 (1993), 70-79.
doi: 10.1017/S1446788700036983. |
[12] |
C. Blair and L. A. Rubel, A triply universal entire function, Enseign. Math. (2), 30 (1984), 269-274. |
[13] |
J. Bonet, Hypercyclic and chaotic convolution operators, J. London Math. Soc., 62 (2000), 253-262.
doi: 10.1112/S0024610700001174. |
[14] |
J. Bonet, Dynamics of the differentiation operator on weighted spaces of entire functions, Math. Z., 261 (2009), 649-677.
doi: 10.1007/s00209-008-0347-0. |
[15] |
J. Bonet and A. Bonilla, Chaos of the differentiation operator on weighted Banach spaces of entire functions, Complex Anal. Oper. Theory, 7 (2013), 33-42.
doi: 10.1007/s11785-011-0134-5. |
[16] |
R. Braun, Weighted algebras of entire functions in which each closed ideal admits two algebraic generators, Michigan Math. J., 34 (1987), 441-450.
doi: 10.1307/mmj/1029003623. |
[17] |
K. G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math., 139 (2000), 47-68. |
[18] |
K. G. Grosse-Erdmann and A. Peris, Linear Chaos, Springer, London, 2011.
doi: 10.1007/978-1-4471-2170-1. |
[19] |
A. Harutyunyan and W. Lusky, On the boundedness of the differentiation operator between weighted spaces of holomorphic functions, Studia Math., 184 (2008), 233-247.
doi: 10.4064/sm184-3-3. |
[20] |
W. Lusky, On the Fourier series of unbounded harmonic functions, J. London Math. Soc., 61 (2000), 568-580.
doi: 10.1112/S0024610799008443. |
[21] |
F. Martínez-Giménez and A. Peris, Chaos for backward shift operators, Int. J. Bifurcation and Chaos, 12 (2002), 1703-1715.
doi: 10.1142/S0218127402005418. |
[22] |
G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal., 98 (1991), 229-269.
doi: 10.1016/0022-1236(91)90078-J. |
[23] |
R. Meise, Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals, J. Reine Angew. Math., 363 (1985), 59-95.
doi: 10.1515/crll.1985.363.59. |
[24] |
R. Meise and B. A. Taylor, Sequence space representations for (FN)-algebras of entire functions modulo closed ideals, Studia Math., 85 (1987), 203-227. |
[25] |
R. Meise and D. Vogt, Introduction to Functional Analysis, The Clarendon Press, Oxford University Press, New York, 1997. |
[26] |
H. Neus, Über die Regularitätsbegriffe induktiver lokalkonvexer Sequenzen, Manuscripta Math., 25 (1978), 135-145.
doi: 10.1007/BF01168605. |
[27] |
E. Wolf, Weighted Fréchet spaces of holomorphic functions, Stud. Math., 174 (2006), 255-275.
doi: 10.4064/sm174-3-3. |
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