Properties of Hilbert spaces, projections and spectral measures are introduced and studied. Spectral integrals and the related operator are considered, and their relationship with the spectrum of an operator is given. The theorems that result yield a version of the spectral theorem which is suited to infinite dimensions.
References
[1]
DeVito, C.L. (1990) Functional Analysis and Linear Operator Theory. Addison-Wesley.
[2]
Halmos, P.R. (1957) Introduction to Hilbert Space and the Theory of Spectral Multiplicity. Chelsea Publisher.
[3]
Helffer, B. (2013) Spectral Theory and Its Applications. Cambridge University Press. https://doi.org/10.1017/cbo9781139505727
[4]
Antunes, P.R.S. and Freitas, P. (2012) Numerical Optimization of Low Eigenvalues of the Dirichlet and Neumann Laplacians. JournalofOptimizationTheoryandApplications, 154, 235-257. https://doi.org/10.1007/s10957-011-9983-3
[5]
Gilkey, P.B. (2004) Asymptotic Formulae in Spectral Geometry (Studies in Advanced Mathematics). Chapman and Hall/CRC.
[6]
Chow, B., Lu, P. and Ni, L. (2006) Hamilton’s Ricci Flow. American Mathematical Society. https://doi.org/10.1090/gsm/077
[7]
Levitin, M., Mangoubi, D. and Polterovich, I. (2023) Graduate Studies in Mathematics, Vol. 237. American Mathematical Society.
[8]
Reed, M. and Simon, B. (1972) Methods of Modern Mathematical Physics. Academic Press.
[9]
Benmerrous, A., Chadli, L.s., Moujahid, A., Elomari, M. and Melliani, S. (2022) Generalized Cosine Family. JournalofEllipticandParabolicEquations, 8, 367-381. https://doi.org/10.1007/s41808-022-00156-x
[10]
Benmerrous, A., Chadli, L., Moujahid, A., Elomari, M. and Melliani, S. (2023) Generalized Fractional Family. International Journal of Difference Equations, 18, 11-34.
