Abstract
In this second part of the book, we assume readers are familiar with notions, properties, and notations about the Fourier transform on L 2, Sobolev spaces and inequalities, absolutely continuous functions, and distributions. Readers who are not accustomed to these concepts are therefore invited to consult the very end of this book, where two small chapters are devoted to them. They should also consult [302, 303], and [326] for further reading.
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References
Engel, K.-J.: Operator matrices and systems of evolution equations, book manuscript (unpublished)
Jin, G., Chen, A.: Some basic properties of block operator matrices. arXiv:1403.7732
Koshmanenko, V.D., Ôta, S.: On the characteristic properties of singular operators. (Ukrainian); translated from Ukraïn. Mat. Zh. 48(11), 1484–1493 (1996). Ukrainian Math. J. 48(11), 1677–1687 (1997)
Möller, M., Szafraniec, F.H.: Adjoints and formal adjoints of matrices of unbounded operators. Proc. Am. Math. Soc. 136(6), 2165–2176 (2008)
Mortad, M.H.: Introductory Topology: Exercises and Solutions, vol. xvii, 2nd edn. (English). World Scientific, Hackensack, NJ (ISBN 978-981-3146-93-8/hbk; 978-981-3148-02-4/pbk), 356 p. (2017)
Mortad, M.H.: An Operator Theory Problem Book. World Scientific Publishing Co., New York (2018). https://doi.org/10.1142/10884. ISBN: 978-981-3236-25-7 (hardcover)
Nagel, R.: Towards a “matrix theory” for unbounded operator matrices. Math. Z. 201(1), 57–68 (1989)
Nagel, R.: The spectrum of unbounded operator matrices with nondiagonal domain. J. Funct. Anal. 89(2), 291–302 (1990)
Ôta, S., Schmüdgen, K.: Some selfadjoint 2 × 2 operator matrices associated with closed operators. Integr. Equ. Oper. Theory 45(4), 475–484 (2003)
Reed, M., Simon, B.: Methods of modern mathematical physics. In: Functional Analysis, vol. 1. Academic Press, New York (1972)
Reed, M., Simon, B.: Methods of modern mathematical physics. Fourier Analysis, Self-Adjointness, vol. 2. Academic Press, New York (1975)
SchmĂĽdgen, K.: Unbounded Self-Adjoint Operators on Hilbert Space, vol. 265. Springer, Berlin (2012). GTM
Taylor, A.E., Lay, D.C.: Introduction to functional analysis. Reprint of the 2nd edn. Robert E. Krieger Publishing Co., Inc., Melbourne, FL (1986)
Tretter, Ch.: Spectral theory of block operator matrices and applications. Imperial College Press, London (2008)
Wright, J.D.M.: All operators on a Hilbert space are bounded. Bull. Am. Math. Soc. 79, 1247–1250 (1973)
Wu, D.Y., Chen, A.: On the adjoint of operator matrices with unbounded entries II. Acta Math. Sin. (Engl. Ser.) 31(6), 995–1002 (2015)
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Mortad, M.H. (2022). Basic Notions. In: Counterexamples in Operator Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-97814-3_18
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