arXiv subjects
Publications and source records attributed to Juan Carlos Sampedro.
This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, the intersection index of algebraic varieties, and the notion of orientability of vector bundles. The novel approach adopted in it facilitates the definition of several invariants closely related to the first Stiefel-Whitney fundamental class through some path integration techniques.
In this paper, we prove a finite dimensional approximation scheme for the Wiener measure on closed Riemannian manifolds, establishing a generalization for $L^{1}$-functionals, of the approach followed by Andersson and Driver on [1]. We follow a new approach motived by categorical concept of colimit.
In this paper we prove an analogue of the uniqueness theorems of Führer and Amann and Weiss to cover the degree of Fredholm operators of index zero of Fitzpatrick, Pejsachowicz and Rabier, whose range of applicability is substantially wider than for the most classical degrees of Brouwer and Leray-Schauder. A crucial step towards the axiomatization of the Fitzpatrick-Pejsachowicz-Rabier degree is provided by the generalized algebraic multiplicity of Esquinas and López-Gómez, $χ$, and the axiomatization theorem of Mora-Corral. The latest result facilitates the axiomatization of the parity of Fitzpatrick and Pejsachowicz, $σ(\cdot,[a,b])$, which provides the key step for establishing the uniqueness of the degree for Fredholm maps.
This paper reveals some new analytical and geometrical properties of the generalized algebraic multiplicity, $χ$, introduced in [7, 5] and further developed in [20, 23, 24]. In particular, it establishes a completely new connection between $χ$ and the concept of local intersection index of algebraic varieties, a central device in Algebraic Geometry. This link between Nonlinear Spectral Theory and Algebraic Geometry provides to $χ$ with a deep geometrical meaning. Moreover, $χ$ is characterized through the new notion of local determinant of the Schur operator associated to the linear path, $\mathfrak{L}(λ)$.
In this article we prove some identities which allow us to evaluate some multiple unit square integrals. In our examples we will give the value of some double and triple integrals. Then, we prove several classical integral formulas with the help of these identities and we present others that seems to be new. Finally we get double integrals for classical constants and different expression for two Ramanujan's integral formulas.