Aigunov Abdullaevich

Analysis of Spectral Charactristics of One Nonself-adjoint Problem: Analysis of Spectral Charactristics of One Nonself-adjoint Problem with Nonsmooth Coefficents Aigunov Abdullaevich

This book is devoted to study of asymptotic behavior of eigenvalues and eigenfunctions of one nonself-adjoint boundary value problem with nonsmooth coefficients, receipt of upper bounds of normalized eigenfunctions in case of summable weight function and establishment of the greatest possible growth rate of eigenfunctions in the considered problem in case of various weight functions. It has been proved that in case of the weight function satisfying Lipschitz condition (in a regular case), normalized eigenfunctions of the problem are uniformly bounded. The results of this book can be used in solution of various problems in mechanics, theory of elasticity, mathematical physics, and optimal control because, as is known, spectral boundary value problems simulate many applications. Can also find their use in mathematics in vindication of Fourier method, in study of convergence of various expansions, etc. This book should be useful in courses on spectral boundary value problems, and generalized problem of evaluation of eigenfunctions in nonself-adjoint boundary value problems.