Research papers in refereed journals

Downloading any publication indicates it is intended for personal non commercial use .

• Del Río R (1988) Ein Gegenbeispiel zur  Stabilität des absolut stetigen Spektrums gewöhnlicher Differentialoperatore (Un contraejemplo a la estabilidad del espectro absolutamente continuo de operadores diferenciales ordinarios), Mathematische Zeitschrift 197: 61-68. [PDF]
• Del Río R (1988) On Conditions which Guarantee Stability of the Absolutely Continuous Spectrum of Differential Operators, Quarterly Journal of Mathematics, Oxford 39: 269-280. [PDF].
• Del Río R (1989) Instability of the Absolutely Continuous Spectrum of Ordinary Differential Operators under Local Perturbations, Journal of Mathematical Analysis and Applications 142: 591-604. [PDF]
• Del Río R. (1990) On Boundary Conditions of An Inverse Sturm-Liouville Problem, SIAM Journal on Applied Mathematics 50: 1745-1751. [PDF]
• Del Río R. (1991) Singular Spectrum of Sturm-Liouville Operators Under Local Perturbations, American Journal of Mathematics 113: 203-217. [PDF]
• Del Río R. (1991) Embedded Eigenvalues of Sturm-Liouville Operators, Communications in Mathematical Physics 142: 421-431. [PDF]
• Del Río R. (1991) Stability of a Singular Continuous Spectrum of Sturm-Liouville Operators, Letters in Mathematical Physics 23: 147-150. [PDF]
• Del Río R. (1994) A Forbidden Set for Embedded Eigenvalues, Proceedings of the  American Mathematical Society 121: 77-82. [PDF]
• Del Río R, Jitomirskaya S, Makarov N, Simon B (1994) Singular Continuous Spectrum is Generic, Bulletin of the American Mathematical Society 31: 208-212. [PDF]
• Del Río R, Makarov N, Simon B (1994) Operators with Singular Continuous Spectrum II: Rank One Operators, Communications in Mathematical Physics 165: 59-67. [PDF]
• Del Río R, Simon B, Stolz G (1994) Stability of Spectral Types for Sturm-Liouville Operators, Mathematical Research Letters 1: 437-450. [PDF]
• Del Río R. Last Y, Jitomirskaya S, Simon B (1995) What is localization?, Physical Review Letters 75: 117-119. [PDF]
• Del Río R, Jitomirskaya S, Last Y, Simon B (1996) Operators with Singular Continuous Spectrum, IV. Hausdorff Dimensions, Rank One Perturbations, and Localization, Journal d' Analyse Mathematique 69: 153-200. [PDF]
• Del Río R, Simon B (1997) Point Spectrum and mixed Spectral Types for Rank one Perturbations, Proceedings of the American Mathematical Society 125: 3593-3599. [PDF]
• Del Río R, Gesztesy F, Simon B (1997) Inverse Spectral Analysis with Partial Information on the Potential III. Updating Boundary Conditions, International Mathematics Research Notices 15: 751-758. [PDF]
• Del Río R, Gesztesy F, Simon B (1998) Corrections and Addendum to Inverse spectral analysis with partial information on the potential III. Updating boundary conditions. Intl Math. Research Notices 11: 623-625, 1999. [PDF]
• Del Río R, Grébert B (2001) Inverse Spectral Results for AKNS Systems with Partial Information on the Potentials. Mathematical Physics, Analysis and Geometry 4: 229-244. [PDF]
• Del Río R, Fuentes S.,Poltoratsky A (2002) Coexistence of spectra in rank-one perturbation problems. Boletin de la Sociedad Matemática Mexicana (3) 8:49-61. [PDF]
• .Del Río R, Tchebotareva O (2003) Boundary conditions of Sturm-Liouville operators with mixed spectra. Journal of Mathematical Analysis and Applications 288: 518-529. [PDF]
• Ricker M, Del Río R (2004) Projecting diameter growth in tropical trees: a new modeling approach.  Forest Science (Society of American Foresters) 50 No. 2: 213-224. [PDF]
• .Del Río R, Kudryavtsev M, Silva L (2006) Rank one perturbations of Jacobi matrices with mixed spectral. Matematische Nachrichten 279 No. 5-6: 502-512. [PDF]
• Del Río R, Tchebotareva O (2007) Sturm-Liouville operators in the half axis with local perturbations. Journal of Mathematical Analysis and Applications 329: 557-566. [PDF]
• Del Río R, Martínez Carmen A (2007) Sturm-Liouville operators in the half axis with shifted potentials. Applicable Analysis 86 No. 10: 1211-1221. [PDF]
• Del Río R, Martínez Carmen, Schulz-Baldes H.(2008) Spectral averaging techniques for Jacobi matrices. Journal of Mathematical Physics. Vol. 49-2:023507-1 - 023507-13. [PDF]
• Damanik D, Del Río R. (2009) Quantum dynamical applications of Salem’s theorem. Letters in Mathematical Physics. Vol. 89-1: 13-19. [PDF]
• Del Río R, Silva L.O.(2011) Spectral measures of Jacobi operators with random potentials. Operators and Matrices.Operators and Matrices . Vol.5,No.3, 435-448 ArXiv
• Del Río R,(2011) Random Sturm Liouville Operators. Applied Mathematics Letters, Vol. 24, No. 2, 179-183 . ArXiv
• Del Rio R , Kudryavtsev, M. (2012) Inverse Problems for Jacobi operators I: Interior mass-spring perturbations in finite systems.Inverse Problems Vol.28, No.5 [ArXiv] [Journal]
• Del Rio R, Kudryavtsev M, Silva L. O.(2012) Inverse problems for Jacobi operators III: Mass-spring perturbations of semi-infinite mass-spring systems. Inverse Problems and Imaging, Vol. 6, No. 4, 599-621. ArXiv
• Del Rio R, Kudryavtsev M, Silva L. O.(2013) Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems.Journal of  Mathematical Physics Analysis and Geometry. Vol.9-2.. 165-190. .ArXiv
• Del Rio R. (2014) Spectra of Random Operators with absolutely continuous Integrated Density of States. Journal of Mathematical Physics 55 (4)04215.Journal ArXiv
• Del Rio R., Silva, L.(2015) Spectral Analysis for linear semi-infinite mass-spring systems. Math. Nachr. 288, No. 11–12, 1241–1253 / DOI 10.1002/mana.201400044.Journal ArXiv
• Del Rio R, Kudryavtsev, M, Silva L. O.(2017) Inverse problems for Jacobi operators IV: Interior mass-spring perturbations of semi-infinite systems.Inverse Problems Volume 33, Number 5 . ArXiv [Journal]
• Del Rio R, Silva L.O. (2018) Stability of determinacy and inverse spectral problems for Jacobi operators Operators and Matrices Vol 12, No 3 pp 619-641. PDF Arxiv
• Bourget O, Cortés V, Del Rio R, Fernández C. (2017) Resonances under Rank One Perturbations. Journal of Mathematical Physics 58, 093502 [Journal] [PDF] Arxiv
• Del Rio R. Franco A, Lara J. (2018) An Aproach to F.Riesz Representation Theorem. CUBO a Mathematical Journal Vol.20, No  02, (01–12). June [Journal]
• Damanik D,Del Rio R,Franco A, Random Sturm-Liouville Operators with Generalized Point Interactions. Oper. Matrices 14 (2020), no. 4, 1101–1125. ArXiv [Journal]
• del Rio, Rafael; Silva, Luis O.; Toloza, Julio H. Point mass perturbations of spectral measures. Rocky Mountain J. Math. 51 (2021), no. 4, 1407–1432. [ArXiv] [Journal]
• Del Rio R, Franco A,  Random Sturm-Liouville Operators with Point Interactions. Math. Nachr. 294 (2021), no. 9, 1684–1701 [ArXiv] [Journal]
• Astaburuaga, A, Cortés V,Fernández C., Del Rio R (2022) Singular Rank One Perturbations. To apear in Journal of Mathematical Physics 58, 093502 [PDF]

Proceedings

 a)  With original results not published elsewhere.

• Del Rio R, (1995) On a Problem of P. Hartman and A. Wintner, Memorias del XXVII Congreso Nacional de la Sociedad Matemática Mexicana, Aportaciones Matemáticas, Serie Comunicaciones 16: 119-123, J. A. Leon, A. Nicolas, F. Ongay, A. Tamariz. Editors. [PDF] .
• Del Rio R, Poltoratski A (1999) Spectral Measures and Category, Operator Theory: Advances and Applications. Birkhauser 108: 149-159. J. Dittrich, P. Exner y M. Tater. Editors. [PDF]
• Del Rio R, Fuentes S, Poltoratski A (2002) Families of Spectral Measures with mixed types. Operator Theory: Advances and Applications. Birkhauser 132: 1311140. Albeverio, Elander, Everett y Kurasov. Editors. [PDF]

b)   Reviews

• Del Rio R. (1988) Inestabilidad del espectro singularmente continuo de operadores diferenciales ordinarios, Memorias del XX Congreso Nacional de la Sociedad Matemática Mexicana, Aportaciones Matemáticas, Serie Comunicaciones 5: 3511360, Marcelo A. Aguilar, Leonardo Salmerón, Cristobal Vargas. Editors. [PDF]
• Del Rio R. (2005) Boundary Conditions and Spectra of Sturm-Liouville Operators. Sturm-Liouville Theory, Past and Present 217-235. W. O. Amrein, A. M. Hinz and D. B. Pearson Editors., Birkhauser, Base. [PDF]

Thesis

B.S. Estudio Matemático de las Ecuaciones de von Kármán. Advisor : Jorge Ize [PDF]

Ph. D. Absolut stetiges Spektrum gewöhnlicher Differentialoperatoren Advisor : Joachim Weidmann [PDF]

Other Publications

• Arredondo J. H. y del Rio R (1990) Expansiones asintóticas para la función de Krein, Universidad Autónoma Metropolitana 1-129.[PDF]
• Del Rio R. y Blancarte H (2000) Solución de un número infinito de desigualdades. Eureka 15: 22-25. [PDF]
  
• Del Rio R y Blancarte H (2001) La densidad integrada de estados para el laplaciano unidimensional. Eureka 18, vol. I p. 4, December 2001.
• Del Rio R, Cruz J y Blancarte H (2003) El espectro del laplaciano unidimensional en diferencias finitas. Eureka 19: 7-15.
• Del Rio R. (1994)  Algunas consideraciones sobre las matemáticas en México. (Some considerations on the mathematical activity in Mexico)  Newspaper  “La Jornada” (October 11,  1994). [PDF] .
• Del Rio R., Franco A.,Lara J.(2016) A direct proof of F. Riesz representation Theorem. ArXiv

Publication edited by IIMAS

Seminario del departamento de Métodos Matemáticos y Numéricos.[PDF]

Señalamientos Metodológicos y Didácticos al tema: Problemas Inversos de la Teoria Espectral [PDF]

Talks in Conferences

Talk video Oaxaca BIRS 2015 http://www.birs.ca/events/2015/5-day-workshops/15w5083/videos/watch/201510011102-delRioCastillo.html

VII Taller-Escuela de Verano de Análisis y Física Matemática 2017

http://www.matcuer.unam.mx/VeranoAnalisis/cursos.html

https://www.youtube.com/results?search_query=iimas+VII+Taller

Congreso SMM-SCM Barranquilla 2018

Congress Barranquilla

 

Last modified:Sept- 2010