My research is focused on advancing our comprehension of analysis and topology within infinite-dimensional spaces, and exploring how this knowledge manifests across diverse mathematical disciplines. These include partial differential equations (PDEs) and constructive quantum field theory.
Although my study is split into two seemingly distinct fields, they share significant intersections that enrich the overall research.
Nonlinear Functional Analysis and Differential Topology:
Topological Degree Theory
Bifurcation Theory on Banach spaces
Nonlinear Spectral Theory and Applications to topological K-Theory
Nonlinear Elliptic & Dispersive Partial Differential Equations
Real and Harmonic Analysis:
Measures on Infinite Dimensional Spaces
Projective Limits of Probability Measures
Wiener Measure on Riemannian Manifolds
Path Integrals and Constructive Quantum Field Theory
D. L. Rodríguez-Vidanes and J. C. Sampedro.
Isometric classification of the Lp-spaces of infinite dimensional Lebesgue measure.
Banach Journal of Mathematical Analysis, Volume 20, (2026), 31 pp.
DOI: doi.org/10.1007/s43037-025-00473-y
ArXiv: arxiv.org/pdf/2503.06217
J. C. Sampedro.
Periodic solutions to nonlocal pseudo-differential equations. A bifurcation theoretical perspective.
Nonlinear Analysis, Volume 254, (2025), 28 pp.
DOI: doi.org/10.1016/j.na.2025.113746
ArXiv: arxiv.org/pdf/2409.04253
J. López-Gómez and J. C. Sampedro.
Blow-up estimates and a priori bounds for the positive solutions of a class of superlinear indefinite elliptic problems.
Nonlinear Analysis, Volume 251, (2025), 9 pp.
DOI: doi.org/10.1016/j.na.2024.113693
ArXiv: arxiv.org/pdf/2402.01519
J. López-Gómez and J. C. Sampedro.
Bifurcation Theory for Fredholm Operators.
Journal of Differential Equations, Volume 404, (2024), 182-250.
DOI: doi.org/10.1016/j.jde.2024.05.040
ArXiv: arxiv.org/pdf/2105.12193
J. C. Sampedro.
On the Lp-spaces of Projective Limits of Probability Measures
Journal of Theoretical Probability, Volume 37, (2024), 2665 to 2703.
DOI: doi.org/10.1007/s10959-024-01329-1
ArXiv: arxiv.org/pdf/2307.12178
J. C. Sampedro.
On the colimits of certain Sobolev spaces,
Journal of Mathematical Analysis and Applications, Volume 535, Issue 2, (2024), 21 pp.
DOI: doi.org/10.1016/j.jmaa.2024.128141
J. C. Sampedro.
Existence of infinite product measures,
Real Analysis Exchange, Volume 42, (2023), 271-284.
DOI: doi.org/10.14321/realanalexch.48.2.1643257005
ArXiv: arxiv.org/pdf/1910.04914
J. López-Gómez and J. C. Sampedro.
Orientability through the algebraic multiplicity,
Journal of Fixed Point Theory and Applications, Volume 25, (2023), 29 pp.
DOI: doi.org/10.1007/s11784-023-01062-y
ArXiv: arxiv.org/pdf/2201.05949
G. Feltrin, J. C. Sampedro and F. Zanolin.
Periodic solutions to superlinear indefinite planar systems: a topological degree approach,
Journal of Differential Equations, Volume 363, (2023), 546-581.
DOI: doi.org/10.1016/j.jde.2023.03.042
ArXiv: arxiv.org/pdf/2211.06070
J. López-Gómez and J. C. Sampedro.
Generating loops and isolas in semilinear elliptic BVP’s,
Nonlinear Analysis, Volume 232, 113268 (2023), 33 pp.
DOI: doi.org/10.1016/j.na.2023.113268
ArXiv: arxiv.org/pdf/2209.04749
J. C. Sampedro.
Approximation schemes for path integration on Riemannian manifolds,
Journal of Mathematical Analysis and Applications, Volume 512, Issue 2 (2022), 19 pp.
DOI: doi.org/10.1016/j.jmaa.2022.126176
ArXiv: arxiv.org/pdf/2106.13905
J. López-Gómez and J. C. Sampedro.
Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier,
Journal of Fixed Point Theory and Applications, Volume 24, Number 8 (2022), 28 pp.
DOI: doi.org/10.1007/s11784-021-00916-7
ArXiv: arxiv.org/pdf/2106.11431
J. López-Gómez and J. C. Sampedro.
New analytical and geometrical aspects of the algebraic multiplicity,
Journal of Mathematical Analysis and Applications, Volume 504, Issue 1 (2021), 21 pp.
DOI: doi.org/10.1016/j.jmaa.2021.125375
ArXiv: arxiv.org/pdf/2012.05671
J. López-Gómez and J. C. Sampedro.
Global perturbation of nonlinear eigenvalues,
Advanced Nonlinear Studies, Volume 21, Issue 2 (2021), 229-249.
DOI: doi.org/10.1515/ans-2021-2127
J. López-Gómez and J. C. Sampedro.
Algebraic multiplicity and topological degree for Fredholm operators,
Nonlinear Analysis, Volume 201, 112019 (2020), 28 pp.
DOI: doi.org/10.1016/j.na.2020.112019
J. C. Sampedro.
On the space of infinite dimensional integrable functions,
Journal of Mathematical Analysis and Applications, Volume 488, Issue 1 (2020), 27 pp.
DOI: doi.org/10.1016/j.jmaa.2020.124043
J. C. Sampedro.
Some identities involving Inverse Gamma integrals,
The Ramanujan Journal, Volume 48, (2019), 577-583.
DOI: doi.org/10.1007/s11139-018-0082-z
J. C. Sampedro.
On a new constant related to Euler’s constant,
The Ramanujan Journal, Volume 46, (2018), 77-89.
DOI: doi.org/10.1007/s11139-017-9912-7
J. C. Sampedro.
Some unit square integrals,
The Ramanujan Journal, Volume 40, (2016), 541-555.
G. Feltrin, J. López-Gómez and J. C. Sampedro.
A proof of a conjecture on the multiplicity of positive solutions of an indefinite superlinear problem, Submitted.
ArXiv: arxiv.org/abs/2501.02854
E. Muñoz-Hernández, J. C. Sampedro and A. Tellini.
Bifurcation Theory for a Class of Periodic Superlinear Problems, Submitted.
ArXiv: arxiv.org/abs/2504.10017
J. C. Sampedro.
Spectral Theory and Bezout Theorem,
Submitted.
ArXiv: arxiv.org/abs/2510.19424
J. López-Gómez and J. C. Sampedro.
Global Leray-Schauder continuation for Fredholm operators, Submitted.
ArXiv: arxiv.org/abs/2512.08412
2024. Premio Extraordinario de Doctorado.
Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid (UCM).
2023. Juan de la Cierva 2022 grants.
Ministerio de Ciencia e Innovación, Gobierno de España.
2nd position in the area of Mathematics.
2022. Egonlabur Fellowship of the Basque Country Government.
Gobierno Vasco. Grant for predoctoral stays.
2021. Kovalevskaya Fellowship for the ICM2022.
Grants for the attendance of young researchers to the ICM2022.
2020. Predoctoral Fellowship of Basque Country Government.
Gobierno Vasco.
The unique grant in the field Mathematics.
2019. PhD initialization Award.
Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid (UCM).
2018. Collaboration Fellowship IKASIKER of the Basque Country Government.
Gobierno Vasco. Director: Luis Escauriaza Zubiria.
2018. Academic Excellence Grant of the Basque Country Government 2017-2018.
Gobierno Vasco
Third position in Science.