Gradinaru, Vasile The Fourier method for abstract equations. (La méthode de Fourier pour des équations abstraites.) (French) Zbl 0885.35022 Ann. Math. Blaise Pascal 3, No. 2, 111-116 (1996). Using a spectral result of the reviewer and S. Sburlan [An. Univ. “Ovidius” Constanta, Ser. Mat. 2, 188-200 (1994; Zbl 0863.46011)], the author studies by the Fourier method the existence and regularity of solutions for first-order abstract differential equations. Applications to the heat equation are also given. Reviewer: Gheorghe Moroşanu (Iaşi) MSC: 35C10 Series solutions to PDEs 34G10 Linear differential equations in abstract spaces Keywords:existence and regularity of solutions; first-order abstract differential equations Citations:Zbl 0863.46011 PDF BibTeX XML Cite \textit{V. Gradinaru}, Ann. Math. Blaise Pascal 3, No. 2, 111--116 (1996; Zbl 0885.35022) Full Text: DOI Numdam EuDML OpenURL References: [1] Kolmogorov, A.N., Fomin, S.V.,“ Elementy teorii funkcij i funkcional”nogo analiza”, Nauka, Moscou, 1989 · Zbl 0672.46001 [2] Lions, J.L., Magenes, E., “Problèmes aux Limites Non Homogènes et Applications”, tome 2, Dunod, Paris1968. · Zbl 0165.10801 [3] Morosanu, Gh.,Sburlan, S. , “Multiple orthogonal seuqences method and applications ”, An.St.Univ. “Ovidius”, Constantza, 3(1995) · Zbl 0882.34062 [4] Nečas, J., “Les méthodes directes en théorie des équations elliptiques”, Masson et Academia, Pariset Prague, 1967 · Zbl 1225.35003 [5] Raviart, P.A., Thomas, J.M., “Introduction à l”analyse numérique des équations aux dérivées partielles”, Masson, Paris, 1988. [6] Yosida, Y., “Functional Analysis”, Springer-Verlag, 1978 · Zbl 0365.46001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.