In this paper, the authors obtain an L^p-version of Green’s Imprimitivity Theorem for the group ℤ of integers. More precisely, for X = ℤ/nℤ and the action α of ℤ on X by translation, it is proved that the full L^p-operator crossed product F^p(ℤ, X, α) is isometrically isomorphic to the spatial L^p-operator tensor product of M_n^p and the reduced group L^p-operator algebra F_λ^p(ℤ). This solves the L^p-imprimitivity problem raised by Phillips for the group of integers. They also prove that F^p(ℤ, X, α) is isometrically isomorphic to C(S¹, M_n^p) precisely when p = 2, where S¹ denotes the unit circle in the complex plane ℂ. Moreover, they determine the K-theory groups of F^p(ℤ, X, α).

Based on both the fundamental theorem of affine geometry in regular L⁰-modules and the recent progress in random convex analysis, this paper characterizes the stable and fully order preserving and order reversing operators acting on the class of proper lower semicontinuous L⁰-convex functions in complete random normed modules.

The paper discusses direct and inverse elastic scattering from a cavity in a homogeneous medium with both Dirichlet and Neumann boundary conditions. Regarding direct scattering, the existence and uniqueness are derived using a variational approach. In the case of inverse scattering, the Fréchet derivatives of the solution operators are investigated, which provides a local stability for the Dirichlet condition.

Leavitt path algebras of bi-separated graphs have been recently introduced by Mohan and Suhas. These algebras provide a common framework for studying various generalisations of Leavitt path algebras. In this paper, the author obtains modules for the Leavitt path algebra L(Ė) of a finitely bi-separated graph Ė = (E, C, D) by introducing the notion of a representation graph for Ė. Among these modules the author finds a class of simple modules. If the bi-separation on E is the Cuntz-Krieger bi-separation (and hence L(Ė) is isomorphic to the usual Leavitt path algebra L(E)), one recovers the celebrated Chen simple modules.

The authors provide a complete characterization of the boundedness and compactness of the Volterra type integration operator T_g from weighted Bergman spaces A_ω^p, induced by doubling weights ω, to Hardy spaces H^q in the unit ball of ℂⁿ, for all 0 < p, q < ∞.

This paper has a twofold purpose. The first is to establish a second main theorem for meromorphic functions on the complex disc Δ(R₀) ⊂ ℂ with finite growth index and small functions, where the counting functions are truncated to level 1 and the small term is more detailedly estimated. The second is to prove a generalization and improvement of the five values theorem of Nevanlinna for the case of five small functions on the complex disc Δ(R₀).

The authors introduce the concept of pure silting complexes and study their main properties. This concept generalizes silting complexes in pure derived category. They also show Bazzoni’s characterization of the pure silting complexes and characterize 2-term pure silting complexes by the connections with the t-structure and torsion pair. Furthermore, they give the Brenner-Butler Theorem about 2-term pure silting complexes.

In this paper, the authors establish some intriguing coincidence best proximity point results for proximal contractions in the context of extended b-metric spaces. They give some illustrative examples from various cases to substantiate their conclusions. The findings discussed in the paper are more general, expanding and enhancing a variety of existing findings in the optimal proximity theory. The findings, which explain the proximal coincidence points for multivalued mappings, are the first of their kind in the current state of the art. In addition, the study provides benchmarks for employing the optimal proximity results once the existence and uniqueness requirements are met.