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192
result(s) for
"Savin, A. Yu"
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Elliptic dilation–contraction problems on manifolds with boundary. C-theory
We study boundary value problems with dilations and contractions on manifolds with boundary. We construct a
C
*- algebra of such problems generated by zero-order operators. We compute the trajectory symbols of elements of this algebra, obtain an analog of the Shapiro–Lopatinskii condition for such problems, and prove the corresponding finiteness theorem.
Journal Article
Elliptic differential dilation–contraction problems on manifolds with boundary
We give a statement of dilation–contraction boundary value problems on manifolds with boundary in the scale of Sobolev spaces. For such problems, we introduce the notion of symbol and prove the corresponding finiteness theorem.
Journal Article
On the symbol of nonlocal operators in Sobolev spaces
We consider nonlocal operators generated by pseudodifferential operators and the operator of shift along the trajectories of an arbitrary diffeomorphism of a smooth closed manifold. We introduce the notion of symbol of such operators acting in Sobolev spaces. As examples, we consider specific diffeomorphisms, namely, isometries and dilations.
Journal Article
Index of nonlocal problems associated with a bundle
We study operators associated with a bundle with compact base and fiber. We construct an algebra of such operators. For elliptic elements of the algebra, we prove the finiteness theorem and derive an index formula.
Journal Article
Index of Sobolev problems on manifolds with many-dimensional singularities
We consider Sobolev spaces on manifolds with many-dimensional singularities. We prove the Fredholm property of such problems and derive the corresponding index formula. The results are based on the theory of translators on manifolds with singularities.
Journal Article
Pseudodifferential operators on stratified manifolds: II
(ProQuest: Abstract omitted; see image)[PUBLICATION ABSTRACT]
Journal Article
Elliptic translators on manifolds with point singularities
We consider translators on manifolds with singularities of the type of a transversal intersection of smooth manifolds. We give the definition of ellipticity of translators, prove the finiteness (Fredholm property) theorem, and establish an index formula for the case of point singularities.
Journal Article
Elliptic translators on manifolds with multidimensional singularities
We consider translators on manifolds with many-dimensional singularities. We state the definition of ellipticity for translators, prove a finiteness (Fredholm property) theorem, and establish an index formula.
Journal Article
On Two Methods of Determining η-Invariants of Elliptic Boundary-Value Problems
For a class of parameter-dependent boundary-value problems that are elliptic in the sense of Agranovich–Vishik, we establish the equality of the
η
-invariant defined in terms of the Melrose regularization and the spectral
η
-invariant of the Atiyah–Patodi–Singer type defined using the analytic continuation of the spectral
η
-function of the operator.
Journal Article
Index formulas for stratified manifolds
We consider elliptic operators on stratified manifolds with stratification of arbitrary length. Under some (symmetry-like) conditions imposed on the symbols of these operators, we obtain index formulas in which the index of an operator is expressed as the sum of indices of some (explicitly written out) elliptic operators on the strata.
Journal Article