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Lead Guest Editor:
Department of Higher Mathematics, Magnitogorsk State Technical University,
A few words about the article: The Laplace operator, its degree and perturbations of this operators cause great interest among researchers. There are many papers devoted to the recovery of such operators from the available spectral data. These are studies that address the so-called inverse spectral problems. Therefore, the spectrum of the Laplace operator or its degree plays a key role in such problems. And since this spectrum is absolutely discrete, the relative position of the points of this spectrum is very important. The spectrum of a degree of the Laplace operator acting on a rectangle is a set of eigenvalues. And these eigenvalues can either coincide with each other, or be as close to each other as you like. Therefore, in any case, the minimum distance between the nearest eigenvalues of the degree of the Laplace operator acting on a rectangle can only be equal to zero. The article is devoted to this fact. Of course, you can solve this problem using cluster analysis methods. However, from a methodological point of view, it is better to use our approach. It is easier for students and graduate students to understand. In addition, in inverse problems using interpolation according to L. Carleson, the smallest distance between the eigenvalues of the unperturbed operator is very important. Therefore, methods similar to the method of L. Carleson cannot be applied to the reconstruction of the perturbed Laplace operator.