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ORDER BY num ASC LIMIT 1' at line 3Array
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[name] => Nonlocal boundary value problems: index theory and semiclassical asymptotics
[seo_title] => Nonlocal boundary value problems: index theory and semiclassical asymptotics
[seo_keywords] => Nonlocal boundary value problems: index theory and semiclassical asymptotics
[seo_description] => Nonlocal boundary value problems: index theory and semiclassical asymptotics
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[cdate] => 2022-10-27 17:17:45
[mdate] => 2026-09-21 12:59:07
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[fulltext] => Nonlocal problems arise in many areas of mathematics, as well as in its applications to science and technology. In this project we focus on nonlocal boundary value problems related to the actions of groups on manifolds. The problem of studying nonlocal elliptic problems is considered. Namely, it is necessary to obtain the concept of a symbol, prove the Fredholm property of elliptic problems, obtain a homotopy classification and present index formulas for new classes of such problems.
In addition, the case of hyperbolic equations (or, more generally, equations with real characteristics) remains practically unexplored in the case of nonlocal problems, mainly due to the complexity of the subject. The task here is to extend existing and well-established methods for local problems, such as Fourier integral operators and the canonical Maslov operator, to cover nonlocal boundary value problems of the types considered here.
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[1] => special domains
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[3] => ellipticity of the index formula
[4] => noncommutative geometry
[5] => semiclassical asymptotics
[6] => Lagrangian manifolds
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