The groundbreaking aspects of this proposal are as follows: (1) development of a unique setup where electrical transport, angle-resolved photoemission (ARPES) and optical spectroscopy is measured in-situ on the same sample, (2) large-area deterministic layer-by-layer growth by chemical vapour deposition (CVD) and molecular beam epitaxy, (3) the effects of mechanical strain and hence large pseudomagnetic fields on the electronic band structure will be investigated using ARPES, (4) the effects of alkali metal doping on the superconducting transition temperature and the

spectral function will be investigated using transport, ARPES and optical spectroscopies shining light onto the superconducting pairing mechanisms in different classes of materials.

In our case, the path of integration always stays on the real axis, and the

spectral function component behavior at the poles is compensated by the subtraction of the specially designed function [19] given by

The aim of the present article is to improve one of the results in [2], where we discussed the asymptotic behavior of the

spectral function of a generalized second-order differential operator.

Thus for -point N sequence the resolution in the spectrum is equal to 1/N The n-th point in the

spectral function corresponds to the frequency f = n/N.

The function [omega] is called a

spectral function for problem (1.

Here [rho], which is called the

spectral function, is right continuous, has jumps at the eigenvalues only, and increases over the continuous spectrum.

To define the singular

spectral function associated with the problem (1.

In this paper we suggest a new numerical algorithm for solving the inverse problem of recovering a singular Sturm- Liouville operator on the half-line from its

spectral function.

Figure 2 also shows the relative

spectral function, s[lambda]), of the emitted (fluorescence) radiation when the excited state returns to the ground state.

In this method, the test functions are selected to be identical as the

spectral functions of decomposition.

These optimal tapers belong to a family of

spectral functions termed discrete prolate spheroidal sequences (DPSS) [29].

2]([xi],[zeta]) are unknown

spectral functions, and indexes 1 and 2 correspond to the TE and TM beams, respectively.