Quadratic Pencil of Schrödinger Operators with Spectral Singularities: Discrete Spectrum and Principal Functions

Spectral Expansion of a Non-Self-Adjoint Differential Operator on the Whole Axis

“…convergence of these integrals in a norm weaker than the norm of L R . 2 For this, we will use the technique of the regularization of divergent integrals. So we will define the following summability factors:…”

An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions

“…Some aspects of this type problems were studied by many authors (see [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]). Such problems play an important role in mathematics and have many applications in natural sciences and engineering.…”

Inverse nodal problem for p_Laplacian diffusion equation with polynomially dependent spectral parameter

“…We note that in this type of problem the spectral parameter is related to the energy of the system, and this motivates the terminology 'energy-dependent'used for the spectral problem of the form (1.4). Inverse problems of quadratic pencil have been studied by numerous authors (see [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]). Inverse spectral problem consists in recovering di¤erential equation from its spectral parameters like eigenvalues, norming constants and nodal points (zeros of eigenfunctions).…”