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The Truncated Fourier Operator. V
Victor Katsnelson, Ronny Machluf
The Fourier operator truncated on a finite symmetric interval is considered. The limiting behavior of its spectrum is discussed as the length of the interval tends to infinity.
The truncated Fourier Operator. IV
V. Katsnelson, R. Machluf
We consider the formal prolate spheroid differential operator on a finite symmetric interval and describe all its self-adjoint boundary conditions. Only one of these boundary condi…
The truncated Fourier operator. III
Victor Katsnelson, Ronny Machluf
The spectral theory of the Fourier operator (non-truncated) is expounded. The known construction of basis of eigenvectors consisting of the Hermite functions is presented. The deta…
The truncated Fourier operator. II
Victor Katsnelson, Ronny Machluf
For (E) being one of the three sets: the whole real axis, a finite symmetric interval and the positive semiaxis, we discuss the simplest differential operators of the second order…
The truncated Fourier operator. I
Victor Katsnelson, Ronny Machluf
Let (\mathscr{F}) be the one dimensional Fourier-Plancherel operator and (E) be a subset of the real axis. The truncated Fourier operator is the operator (\mathscr{F}_E) of the for…