Extensiones disipativas de relaciones simétricas mediante tripletes fronterizos

Josué Ivan Rios-Cangas

doi:10.29057/icbi.v13iEspecial.13520

Autores/as

Josué Ivan Rios-Cangas Universidad Autónoma Metropolitana l Unidad Iztapalapa l México. https://orcid.org/0000-0001-7758-7362

DOI:

https://doi.org/10.29057/icbi.v13iEspecial.13520

Palabras clave:

Relaciones lineales, relaciones disipativas, teoría de extensión, tripletes fronterizos

Resumen

El concepto de relación lineal extiende la noción de operador lineal. Además, las relaciones lineales disipativas están estrechamente relacionadas con los sistemas en donde la energía no aumenta a través del tiempo, en particular, con los sistemas conservativos. Con base en la teoría de tripletes fronterizos, este trabajo estudia extensiones disipativas de relaciones lineales simétricas.

Descargas

Los datos de descargas todavía no están disponibles.

Información de Publicación

Este artículo

Otros artículos

Revisores por pares

Revisores: 1

2.4 promedio

Perfiles de revisores N/D

Declaraciones del autor

Disponibilidad de datos

N/A

16%

Financiamiento externo

No

32% con financiadores

Intereses conflictivos

N/D

11%

Para esta revista

Otras revistas

Artículos aceptados

86%

33%

Días hasta la publicación

250

145

Indexado en

GS

Editor y comité editorial: perfiles
Sociedad académica: N/D
Editora:: Universidad Autónoma del Estado de Hidalgo

Citas

Acharya, K. R. (2014). Self-adjoint extension and spectral theory of a linear relation in a Hilbert space. ISRN Math. Anal., pages Art. ID 471640, 5.

Arens, R. (1961). Operational calculus of linear relations. Pacific J. Math., 11:9-23.

Azizov, T. Y., Dijksma, A., and Wanjala, G. (2013). Compressions of maximal dissipative and self-adjoint linear relations and of dilations. Linear Algebra Appl., 439(3):771–792.

Birman, M. S. and Solomjak, M. Z. (1987). Spectral theory of selfadjoint operators in Hilbert space. Mathematics and its Applications (Soviet Series). D. Reidel Publishing Co., Dordrecht. Translated from the 1980 Russian original by S. Khrushchev and V. Peller.

Bolaños Servín, J. R., Quezada, R., and Rios-Cangas, J. I. (2023). Elementos Matemáticos de la Mecánica Cuántica. Revista Metropolitana de Matemáticas - Mixba'al, 14(1):143-222.

Calkin, J. W. (1939). Abstract symmetric boundary conditions. Trans. Amer. Math. Soc., 45(3):369–442.

Coddington, E. A. (1973). Extension theory of formally normal and symmetric subspaces. American Mathematical Society, Providence, R.I. Memoirs of the American Mathematical Society, No. 134.

Cross, R. (1998). Multivalued linear operators, volume 213 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York.

Cross, R., Favini, A., and Yakubov, Y. (2011). Perturbation results for multivalued linear operators. In Parabolic problems, volume 80 of Progr. Nonlinear Differential Equations Appl., pages 111–130. Birkhauser ̈ /Springer Basel AG, Basel.

Derkach, V. (2015). Boundary Triplets, Weyl Functions, and the Kre ̆ın Formula, pages 183–218. Springer Basel, Basel. Derkach, V., Hassi, S., and Malamud, M. (2020). Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions. Math. Nachr., 293(7):1278–1327.

Derkach, V., Hassi, S., and Malamud, M. (2022). Generalized boundary triples, II. Some applications of generalized boundary triples and form domain invariant Nevanlinna functions. Math. Nachr., 295(6):1113–1162.

Derkach, V. A. and Malamud, M. M. (1991). Generalized resolvents and the boundary value problems for Hermitian operators with gaps. J. Funct. Anal., 95(1):1–95.

Derkach, V. A. and Malamud, M. M. (1995). The extension theory of Hermitian operators and the moment problem. J. Math. Sci., 73(2):141–242. Analysis. 3.

Dijksma, A. and de Snoo, H. S. V. (1974). Self-adjoint extensions of symmetric subspaces. Pacific J. Math., 54:71-100.

Fernandez Miranda, M. and Labrousse, J.-P. (2005). The Cayley transform of linear relations. Proc. Amer. Math. Soc., 133(2):493-499.

Gorbachuk, V. I. and Gorbachuk, M. L. (1991). Boundary value problems for operator differential equations, volume 48 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht. Translated and revised from the 1984 Russian original.

Hassi, S., De Snoo, H., and Winkler, H. (2000a). Boundary-value problems for two-dimensional canonical systems. Integral Equations Operator Theory, 36(4):445–479.

Hassi, S., Remling, C., and de Snoo, H. (2000b). Subordinate solutions and spectral measures of canonical systems. Integral Equations Operator Theory, 37(1):48–63.

Hassi, S., Sebestyn, Z., de Snoo, H. S. V., and Szafraniec, F. H. (2007). A canonical decomposition for linear operators and linear relations. Acta Math. Hungar., 115(4):281-307.

Jurˇ senas, R. (2023). On the similarity of boundary triples of symmetric operators in Krein spaces. Complex Anal. Oper. Theory, 17(5):Paper No. 72, 39.

Koˇ cube ̆i, A. N. (1975). Extensions of symmetric operators and of symmetric binary relations. Mat. Zametki, 17:41–48.

Krein, M. G. and Langer, G. K. (1971). The defect subspaces and generalized resolvents of a Hermitian operator in the space I‹. Funkcional. Anal. iPrilozen, 5（2）：59-71.

Kre ̆ in, M. G. and Langer, G. K. (1971). The defect subspaces and generalized resolvents of a Hermitian operator in the space Πκ. Funkcional. Anal. i Priloˇzen., 5(3):54–69.

Phillips, R. S. (1959). Dissipative operators and hyperbolic systems of partial differential equations. Trans. Amer. Math. Soc., 90:193-254.

Rios-Cangas, J. I. (2021). Operadores simétricos multivaluados y el problema de momentos de Hamburger truncado. Revista Metropolitana de Matemáticas - Mixba'al, 12(1):33-45.

Rios-Cangas, J. I. and Silva, L. O. (2020). Dissipative extension theory for linear relations. Expo. Math., 38(1):60-90.

Schmüdgen, K. (2012). Unbounded self-adjoint operators on Hilbert space, volume 265 of Graduate Texts in Mathematics. Springer, Dordrecht.

Sz.-Nagy, B. (1953). Sur les contractions de l'espace de Hilbert. Acta Sci. Math. Szeged, 15:87-92.

von Neumann, J. (1930). Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren. Math. Ann., 102(1):49-131.

von Neumann, J. (1950). Functional Operators. II. The Geometry of Orthogonal Spaces. Annals of Mathematics Studies, no. 22. Princeton University Press, Princeton, N. J.