Sentence examples for unbounded spectra from inspiring English sources
We discuss a sharp contrast between the cases of compact and unbounded spectra.
Errors in calculating the discrete Hilbert Transform (HT) of a signal arise from three main reasons: (1) end effects: due to the finite duration of the signal, (2) discretization: through the sampling process, and (3) the Bedrosian identity is not satisfied because the exponential function has an unbounded spectrum.
Note that the Wiener phase noise spectrum becomes unbounded at, which is a consequence of the variance increasing linearly with time.
This provides a new method to enclose the spectrum of unbounded block operator matrices by means of the non-convex set W2(A).
In this paper we establish a new analytic enclosure for the spectrum of unbounded linear operators A admitting a block operator matrix representation.
The spectrum of an unbounded operator is defined in precisely the same way as for bounded operators: λ is a spectral value if the resolvent operator R_\lambda = (T-\lambda)^{-1} fails to be a well-defined continuous operator.
This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator.
Performance gain in the turbulent case is assessed by comparing scalar energy and dissipation spectra produced by several bounded and unbounded schemes.
However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below.
We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators Aj on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula.
For an arbitrary linear (possibly unbounded) operator A on a Banach space, with real spectrum, we construct a maximal continuously embedded Banach subspace on which this operator has a Cℓ(R) functional calculus.
