Victor Ivrii Livres

Focusing on semiclassical microlocal analysis, this five-volume monograph aims to derive precise spectral asymptotics for various partial differential operators. It explores the propagation of singularities and employs variational estimates in small domains to examine more complex domains with differing singularities. The developed theories and methods are then applied to the Magnetic Schrödinger operator and various challenges in multiparticle quantum theory, offering significant insights into these advanced mathematical concepts.

Focusing on the derivation of sharp spectral asymptotics, this comprehensive five-volume monograph utilizes semiclassical microlocal analysis techniques, particularly the propagation of singularities. It explores variational estimates in small domains, extending to domains with various singularities. The developed theory is then applied to the Magnetic Schrödinger operator, addressing diverse problems and aspects of multiparticle quantum theory, offering valuable insights into the behavior of partial differential operators.

Focusing on the derivation of sharp spectral asymptotics, this comprehensive five-volume monograph employs semiclassical microlocal analysis techniques, particularly the propagation of singularities. It explores variational estimates in small domains, extending the analysis to domains with various singularities. The developed general theory is applied to the Magnetic Schrödinger operator and addresses diverse problems in multiparticle quantum theory, showcasing the intersection of advanced mathematics and physics.

Focusing on advanced spectral asymptotics, this comprehensive five-volume monograph employs semiclassical microlocal analysis techniques, particularly the propagation of singularities. It explores variational estimates in small domains to address more complex domains featuring various singularities. The theoretical framework developed is then applied to the Magnetic Schrödinger operator, alongside a range of problems in multiparticle quantum theory, showcasing the broad applicability of the results and methods derived throughout the work.

Focusing on semiclassical microlocal analysis, this five-volume monograph derives sharp spectral asymptotics for various partial differential operators. It emphasizes the propagation of singularities and employs variational estimates in small domains to explore domains with different singularities. The developed methods and results are applied to the Magnetic Schrödinger operator and various problems in multiparticle quantum theory, showcasing a rigorous approach to complex mathematical concepts in spectral theory.

The problem of spectral asymptotics, in particular the problem of the asymptotic dis tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; moreover, it is very important for the general theory of partial differential operators. I started working in this domain in 1979 after R. Seeley found a remainder estimate of the same order as the then hypothetical second term for the Laplacian in domains with boundary, and M. Shubin and B. M. Levitan suggested that I should try to prove Weyl's conjecture. During the past fifteen years I have not left the topic, although I had such intentions in 1985 when the methods I invented seemed to fai! to provide furt her progress and only a couple of not very exciting problems remained to be solved. However, at that time I made the step toward local semiclassical spectral asymptotics and rescaling, and new horizons opened.