@article{CM_1986__57_1_15_0, author = {Chojnacki, Wojciech}, title = {Fonctions cosinus hilbertiennes born\'ees dans les groupes commutatifs localement compacts}, journal = {Compositio Mathematica}, pages = {15--60}, publisher = {Martinus Nijhoff Publishers}, volume = {57}, number = {1}, year = {1986}, mrnumber = {817295}, zbl = {0591.47030}, language = {fr}, url = {http://www.numdam.org/item/CM_1986__57_1_15_0/} }
TY - JOUR AU - Chojnacki, Wojciech TI - Fonctions cosinus hilbertiennes bornées dans les groupes commutatifs localement compacts JO - Compositio Mathematica PY - 1986 SP - 15 EP - 60 VL - 57 IS - 1 PB - Martinus Nijhoff Publishers UR - http://www.numdam.org/item/CM_1986__57_1_15_0/ LA - fr ID - CM_1986__57_1_15_0 ER -
Chojnacki, Wojciech. Fonctions cosinus hilbertiennes bornées dans les groupes commutatifs localement compacts. Compositio Mathematica, Tome 57 (1986) no. 1, pp. 15-60. http://www.numdam.org/item/CM_1986__57_1_15_0/
[1] D'Alembert's functional equation in Banach algebras. Acta Sci. Math. (Szeged) 32 (1971) 225-234. | MR | Zbl
:[2] Cosine, exponential and quadratic functions. Glas. Math. Ser. III 16 (1981) 269-274. | MR | Zbl
et :[3] Theory of Group Representations and Applications. Warszawa: Polish Scientific Publishers (1980). | MR | Zbl
et :[4] Spectral Synthesis. Stuttgart: Teubner (1975). | MR | Zbl
:[5] Eléments de mathématique, Intégration, Chapitre V: Intégration des mesures. Paris: Hermann (1967). | MR | Zbl
:[6] On the cosine-sine operator functional equations. Aequations Math. 6 (1971) 231-234. | MR | Zbl
:[7] On the measurability and continuity properties of the cosine operator. Indian J. Pure Appl. Math. 12 (1981) 81-83. | MR | Zbl
et :[8] Una caratterizzazione dei generatori di funzioni coseno astratte. Boll. Un. Mat. Ital. 22 (1967) 357-362. | MR | Zbl
et :[9] Ergodic theorems for abelian semigroups. Trans. Amer. Math. Soc. 51 (1942) 399-412. | JFM | MR | Zbl
:[10] Les moyennes invariantes dans les semi-groupes et leurs applications. Acta Sci. Math. (Szeged) 12 A (1950) 213-227. | MR | Zbl
:[11] Aproximation and representations for Fourier transforms. Trans. Amer. Math. Soc. 153 (1971) 211-221. | MR | Zbl
:[12] Linear Operators, Part III: Spectral Operators. New York: Wiley-Interscience (1971). | MR | Zbl
et :[13] A note on Fourier-Stieltjes transforms. Proc. Amer. Math. Soc. 6 (1955) 310-312. | MR | Zbl
:[14] Ordinary differential equations in linear topological spaces. I. J. Differential Equations 5 (1968) 72-105. | Zbl
:[15] Ordinary differential equations in linear topological spaces. II. J. Differential equations 6 (1969) 50-70. | Zbl
:[16] Uniformly bounded cosine functions in Hilbert space. Indiana Univ. Math. J. 20 (1970) 411-425. | MR | Zbl
:[17] Some remarks on second-order abstract Cauchy problems. Funkcial. Ekvac. 24 (1981) 331-344. | MR | Zbl
:[18] Cosine representations of abelian *-semigroups and generalized cosine operator functions. Canad. J. Math. 30 (1978) 474-482. | MR | Zbl
et :[19] A commutativity theorem for normal operators. Proc. Amer. Math. Soc. 36 (1950) 35-40. | MR | Zbl
:[20] Funzioni coseno periodiche. Boll. Un. Mat. Ital. 22 (1967) 478-485. | MR | Zbl
:[21] Semigroups and second-order differential equations. J. Funct. Anal. 4 (1969) 50-70. | MR | Zbl
:[22] On a connection between first and second order differential equations in Banach spaces. J. Math. Anal. Appl. 30 (1970) 246-251. | MR | Zbl
:[23] On the convergence and approximation of cosine functions. Aequationes Math. 10 (1974) 201-205. | MR | Zbl
:[24] Convergence rates of ergodic limits for semigroups and cosine functions. Semigroup Forum 16 (1978) 89-95. | MR | Zbl
, Ch. RADIN et :[25] Essays in Commutative Harmonic Analysis. New York: Springer (1979). | MR | Zbl
et :[26] Three results on I-sets, Colloq. Math. (à paraître). | MR | Zbl
et :[27] Invariant Means on Topological Groups and Their Applications. New York: Van Nostrand (1969). | MR | Zbl
:[28] Abstract Harmonic Analysis, Volumes I et II. Berlin: Springer (1963 et 1970). | MR | Zbl
et :[29] Real and Abstract Analysis. Berlin: Springer (1969). | MR | Zbl
et :[30] The functional equation f(xy)+f(xy-1)=2f(x)f(y) for groups. Proc. Amer. Math. Soc. 19 (1968) 69-74. | MR | Zbl
:[31] On second order Cauchy's problem in a Banach space. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970) 371-374. | MR | Zbl
:[32] On operator-valued solutions of d'Alembert's functional equation I. Colloq. Math. 23 (1971) 107-114. | MR | Zbl
:[33] On operator-valued solutions of d'Alembert's functional equation II. Studia Math. 42 (1972) 43-66. | MR | Zbl
:[34] On cosine operator functions and one-parameter groups of operators. Studia Math. 44 (1972) 93-105. | MR | Zbl
:[35] Cosine functions of operators in locally convex spaces. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 18 (1971/72) 443-463. | MR | Zbl
:[36] A cosine functional equation in n-dimensional vector space. Glasnik Mat.-Fiz. Astronom. Ser. II Društvo Mat. Fiz. Hrvatske 13 (1958) 169-189. | MR | Zbl
:[37] A cosine functional equation in Hilbert space. Canad. J. Math. 19 (1960) 45-50. | MR | Zbl
:[38] On some functional equations in Banach spaces. Studia Math. 19 (1960) 149-158. | MR | Zbl
:[39] A cosine functional equation in Banach algebras. Acta Sci. Math. (Szeged) 23 (1962) 255-267. | MR | Zbl
:[40] Uniformly bounded cosine function in a Banach space. Math. Balkanica 2 (1972) 109-115. | MR | Zbl
:[41] Weakly measurable selfadjoint cosine function. Glas. Mat. Ser. III 8 (1973) 73-79. | MR | Zbl
:[42] Decomposition of weakly measurable semigroups and cosine operator functions. Glas. Mat. Ser. III 11 (1976) 91-95. | MR | Zbl
:[43] Semigroups and cosine functions. Functional Analysis; Proceedings of a conference held at Dubrovnik, Yugoslavia, 1981. Lecture Notes in Math. 948 (1982) 48-72. | MR | Zbl
:[44] Which operators generate cosine operator functions? Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 63 (1978) 314-317. | MR | Zbl
:[45] Compactness properties of operator cosine functions. C. R. Math. Rep. Acad. Sci. Canada 2 (1980) 277-280. | MR | Zbl
:[46] Über operatorwertige Lösungen der Funktionalgleichung des Cosinus. Math. Z. 171 (1980) 233-245. | MR | Zbl
:[47] Periodische operatorwertige Cosinusfunktionen. Resultate Math. 4 (1981) 75-83. | MR | Zbl
:[48] On bounded time-dependent perturbations of operator cosine functions. Aequationes Math. 23 (1981) 197-203. | MR | Zbl
:[49] Strongly continuous operator cosine functions. Functional Analysis; Proceedings of a conference held at Dubrovnik, Yugoslavia, 1981. Lecture Notes in Math. 948 (1982) 73-97. | MR | Zbl
:[50] Über die Konvergenz operatorwertiger Cosinusfunktionen mit gestortem infinitesimalen Erzeuger. Period. Math. Hungar. 14 (1983) 101-105. | MR | Zbl
:[51] Spectral representations for solutions of certain abstract functional equations. Compositio Math. 15 (1962) 1-22. | Numdam | MR | Zbl
:[52] Spectral representations for some unbounded normal operators. Trans. Amer. Math. Soc. 110 (1964) 79-87. | MR | Zbl
:[53] Pontryagin Duality and the Structure of Locally Compact Abelian Groups. Cambridge: Cambridge University Press (1977). | MR | Zbl
:[54] On the generators of cosine operator functions. Publ. Math. Debrecen 21 (1974) 151-154. | MR | Zbl
:[55] On cosine operator functions in Banach spaces. Acta Sci. Math. (Szeged) 36 (1974) 281-289. | MR | Zbl
:[56] Cosine operator functions and the abstract Cauchy problem. Period. Math. Hungar. 7 (1976) 213-217. | MR | Zbl
:[57] Approximation theorems for cosine operator functions. Acta Math. Acad. Sci. Hungar. 29 (1977) 69-76. | MR | Zbl
:[58] Analytic properties of cosine operators. Proc. Amer. Math. Soc. 74 (1979) 101-104. | MR | Zbl
et :[59] On normal operator in Hilbert space. Amer. J. Math. 73 (1951) 357-362. | MR | Zbl
:[60] A remark on cosine families. Proc. Amer. Math. Soc. 79 (1980) 376-378. | MR | Zbl
:[61] On a theorem of Fuglede and Putnam. J. London Math. Soc. 33 (1958) 376-377. | MR | Zbl
:[62] A note on the cosine equation for probability on compact semigroups. Glas. Mat. Ser. III 15 (1980) 383-385. | MR | Zbl
:[63] Cosine operator functions. Dissertationes Math. (Rozprawy Mat.) 49 (1966) 1-47. | MR | Zbl
:[64] Semigroups and cosine functions of normal operators in Hilbert spaces. Časopis Pěst. Mat. 93 (1968) 437-458. | MR | Zbl
:[65] A Phillips-Miyadera type perturbation theorem for cosine functions of operators. Tôhuku Math. J. 30 (1978) 107-115. | MR | Zbl
et :[66] Compactness, regularity, and uniform continuity properties of strongly continuous cosine families. Houston J. Math. 3 (1977) 555-567. | MR | Zbl
et :[67] Cosine families and abstract nonlinear second order differential equations. Acta Math. Acad. Sci. Hungar. 32 (1978) 75-96. | MR | Zbl
et :[68] An abstract second order semilinear Volterra integrodifferential equation. SIAM J. Math. Anal. 10 (1978) 412-424. | MR | Zbl
et :[69] On the analogue of the formula cos t = 12eit + 12e-it for operator cosine functions. Comment. Math. Prace Mat. 23 (1983) 173-182. | MR | Zbl
:[70] Einige Funktionalgleichungen im Fréchetschen Raum. Glas. Mat. Ser. III 3 (1968) 19-40. | MR | Zbl
:[71] Commuting spectral measures on Hilbert space. Pacific J. Math. 4 (1954) 355-361. | MR | Zbl
: