https://hdl.handle.net/10481/31357 2026-04-11T12:25:30Z https://hdl.handle.net/10481/112308 The uniform strong diameter two property Martínez Vañó, Esteban; Rueda Zoca, Abraham We study a uniform version of the strong diameter two property. In particular, we find a characterisation that does not involve ultrafifilters and we use it to provide some examples of spaces with this uniform property that do not follow from previously known results. https://hdl.handle.net/10481/112099 The uniform strong diameter two property Martínez Vañó, Esteban; Rueda Zoca, Abraham We study a uniform version of the strong diameter two property. In particular, we find a characterisation that does not involve ultrafilters and we use it to provide some examples of spaces with this uniform property that do not follow from previously known results. https://hdl.handle.net/10481/109253 Nonlocal operators in divergence form and existence theory for integrable data Arcoya Álvarez, David; Dipierro, Serena; Proietti Lippi, Edoardo; Sportelli, Caterina; Valdinoci, Enrico We present an existence and uniqueness result for weak solutions of Dirichlet boundary value problems governed by a nonlocal operator in divergence form and in the presence of a datum which is assumed to belong only to L1(Ω) and to be suitably dominated. We also prove that the solution that we find converges, as s ↗1, to a solution of the local counterpart problem, recovering the classical result as a limit case. This requires some nontrivial customized uniform estimates and representation formulas, given that the datum is only in L1(Ω) and therefore the usual regularity theory cannot be leveraged to our benefit in this framework. The limit process uses a nonlocal operator, obtained as an affine transformation of a homogeneous kernel, which recovers, in the limit as s ↗ 1, every classical operator in divergence form. https://hdl.handle.net/10481/108730 Extending Segal’s postulates of quantum mechanics to the complex case Velasco Collado, María Victoria; Aycart-Maldonado, Enrique In this paper, we review Segal’s postulates for general Quantum Mechanics, updating and clarifying their mathematical formulation to simplify them. Our approach provides additional insights as well as a pathway to easily contribute new results to the body of knowledge on systems of observables. Moreover, we introduce the notion of complex system of observables, which arises naturally from the analysis carried out. As we show, these last systems of observables are related to the classical (real) ones through the process of complexification. Taking advantage of this, algebraic systems of observables are completely determined in both the real and complex cases. Funding for open access publishing: Universidad de Granada/CBUA. This study was funded by Vicerrectorado de Investigación y Transferencia, Universidad de Granada and Instituto de Matemáticas, Universidad de Granada (Maria de Maeztu). https://hdl.handle.net/10481/108402 Bifurcation in two parameters for a quasilinear Schrödinger equation Arcoya Álvarez, David; Carmona, José; Martínez-Teruel, Miguel This paper deals with existence and multiplicity of positive solutions for the quasilinear Schrödinger equation. We use bifurcation theory to analyze the set of positive solutions. This research has been funded by Junta de Andalucía (grant FQM-116), by the Spanish Ministry of Science and Innovation, Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (grant PID2021-122122NB-I00) and by the FPU predoctoral fellowship of the Spanish Ministry of Universities (FPU21/05578).