After Hilbert's initial formulation, the later development of abstract Hilbert space and the spectral theory of a single normal operator on it did very much go in parallel with the requirements of physics; particularly in the hands of von Neumann.
42.
The Hecke operators, which act on the space of all cusp forms, preserve the subspace of newforms and are spectral theory of such operators, there exists a basis for the space of newforms consisting of eigenforms for the full Hecke algebra.
43.
He has performed research in various areas of mathematics and the applied sciences such as non-self-adjoint operator theory, multiparameter spectral theory, the theory of joint spectra, differential equations, numerical ranges, and mathematical models of economy.
44.
"' Kalyan Bidhan Sinha ( K . B . Sinha ) "'( born 3 June 1944 ) is an Indian mathematician who specialised in mathematical theory of scattering, spectral theory of Schr�dinger operators, and quantum stochastic processes.
45.
He proposed as a generalization of eigenvalues, the concept of the spectrum of an operator, in an 1897 paper; the concept was further extended by David Hilbert and now it forms the main object of investigation in the field of spectral theory.
46.
This series really comes up in rather specialized applications to spectral theory, where one would like to assign a finite value to something that turns out to actually be infinite ( like a trace of an operator that isn't properly trace class ).
47.
Spectral theory of a simple kind applies, to show that " L " acts via a basis of eigenvectors; in other words " L " has an action that is via diagonal matrices on the holomorphic vector fields on " A ".
48.
He is Editor-in-Chief of Acta Mathematica, Editor-in-Chief of Arkiv f�r Matematik, Deputy Chief Editor of the " Journal of Spectral Theory ", Editor of the " Bulletin of Mathematical Sciences ", Editor of " Problems in Mathematical Analysis ", and Editor of " Izvestiya Vysshikh Uchebnykh Zavedenii.
49.
"' Mark Kac "'(; Can one hear the shape of a drum ? " set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry . ( In the end, the answer was " no ", in general .)
50.
"' Friedrich " Fritz " Gesztesy "'( born 5 November 1953, Austria ) is a well-known Austrian-American mathematical physicist and Professor of Mathematics at Baylor University, known for his important contributions in spectral theory, functional analysis, partial differential operators, and completely integrable systems ( soliton equations ).
