Abstract
In this monograph, we mainly handle real Banach spaces and Hilbert spaces and real linear operators. For this reason, Banach spaces, Hilbert spaces and linear operators always mean real ones if they are not otherwise specified. However, they are all obtained as a real part (in a certain sense) of some complex Banach spaces, Hilbert spaces or complex linear operators. This means that we can fortunately utilize the powerful tools developed in Complex Functional Analysis. The first half of this chapter is devoted to reviewing the most convenient way to utilize the tools of Complex Functional Analysis to real spaces and operators. These results were originally presented in the paper (Yagi (Bull South Ural State Univ Ser MMCS 10:97–112, 2017)).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations (Springer, Berlin, 2011)
R. Dautray, J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, vol. 1 (Masson, Paris, 1984)
R. Dautray, J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, vol. 2 (Masson, Paris, 1984)
J.L. Lions, E. Magenes, Problème aux limites non homogènes et applications, vol. 1 (Dunord, Paris, 1968)
S. Łojasiewicz, Une propriété topologique des sous-ensembles analytique réels. Colloques internationaux du C.N.R.S.: Les équations aux dérivées partielles, Paris, 1962 (Editions du C.N.R.S., Paris, 1963), pp. 87–89
S. Łojasiewicz, Ensembles Semi-Analytiques (Publ. Inst. Hautes Etudes Sci., Bures-sur-Yvette, 1965)
S. Łojasiewicz, M.A. Zurro, On the gradient inequality. Bull. Polish Acad. Sci. Math. 47, 143–145 (1999)
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators (North-Holland, Amsterdam, 1978)
A. Yagi, Abstract Parabolic Evolution Equations and their Applications (Springer, Berlin, 2010)
A. Yagi, Real sectorial operators. Bull. South Ural State Univ. Ser. MMCS 10, 97–112 (2017)
A. Yagi, Abstract Parabolic Evolution Equations and the Łojasiewicz–Simon Gradient Inequality, Applications, vol. 2, (Springer, Berlin, to appear)
K. Yosida, Functional Analysis, 6th edn. (Springer, Berlin, 1980)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Yagi, A. (2021). Preliminaries. In: Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I. SpringerBriefs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-16-1896-3_1
Download citation
DOI: https://doi.org/10.1007/978-981-16-1896-3_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-1895-6
Online ISBN: 978-981-16-1896-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)