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Bernstein-nikolskii-stechkin inequality and Jackson’s theorem for the index Whittaker transform
In this paper, by using the Whittaker translation operators studied recently by Sousa et al., we define the modulus of smoothness associated with the...
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Complements, index theorem, and minimal log discrepancies of foliated surface singularities
We present an extension of several results on pairs and varieties to foliated surface pairs. We prove the boundedness of local complements, the local...
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An Index Theorem for Linear Relations and Its Applications to the Study of Block Relation Matrices
AbstractIn this paper, we aim to prove an index theorem for linear relations and apply it to study the invertibility and the essential invertibility...
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The Relative Index Theorem for General First-Order Elliptic Operators
The relative index theorem is proved for general first-order elliptic operators that are complete and coercive at infinity over measured manifolds....
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On the Poincaré–Bendixson Index Theorem for a Class of Piecewise Linear Differential Systems
Poincaré–Bendixson index theorem showed that: if planar smooth differential systems have only finitely number of singular points inside a limit...
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The Index Theorem of Atiyah and Singer
The elliptic operator \(D = d/dx\) acting on the circle...
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Witten deformation on non-compact manifolds: heat kernel expansion and local index theorem
Asymptotic expansions of heat kernels and heat traces of Schrödinger operators on non-compact spaces are rarely explored, and even for cases as...
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Relative equivariant coarse index and relative L2-index
In this paper, we define a relative equivariant coarse index for proper actions and a relative L 2 -index. We derive a relative equivariant coarse...
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A decomposition theorem for unitary group representations on Kaplansky–Hilbert modules and the Furstenberg–Zimmer structure theorem
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky–Hilbert modules over Stone algebras is...
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The s-Cobordism Theorem
In this chapter we want to discuss and prove the following theorem (in the smooth category).
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Hahn–Banach Theorem
The notion of extension in continuity of a linear continuous functional is introduced an famous Hahn-Banach theorem is formulated, together with...
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The higher fixed point theorem for foliations: applications to rigidity and integrality
We give applications of the higher Lefschetz theorems for foliations of Benameur and Heitsch (J. Funct. Anal. 259:131–173, 2010), primarily involving...
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O’Neill’s theorem for PL approximations
We present a version of O’Neill’s theorem (Theorem 5.2 in O’Neill in Am J Math 75(3):497–509, 1953) for piecewise linear approximations.
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An Introduction to Index Theory and Noncommutative Geometry
In this chapter we introduce some of the basic ideas of Index Theory and of the Noncommutative Geometry of Alain Connes. Our main specific objective...
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𝑩2 index
In addition to the 𝑩1 index, Shao and Sokal [137] introduced the 𝑩2 index as a measure of tree balance. Bienvenu et al. [13] later found that, due...
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An equivariant Atiyah–Patodi–Singer index theorem for proper actions II: the K-theoretic index
Consider a proper, isometric action by a unimodular locally compact group G on a Riemannian manifold M with boundary, such that M / G is compact. Then...
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The Classical Galois Theorem
This first chapter presents the classical Galois theorem for fields. A finite-dimensional extension of fields K ⊆ L is a Galois extension when every...
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The index of certain Stiefel manifolds
This paper computes the Fadell–Husseini index of Stiefel manifolds in the case where the group acts via permutations of the orthogonal vectors. The...
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A Birkhoff–Kellogg Type Theorem for Discontinuous Operators with Applications
By means of fixed point index theory for multivalued maps, we provide an analogue of the classical Birkhoff–Kellogg Theorem in the context of...
