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La figura espectral del producto tensorial de dos operadores.

Carlos Bosch Giral, Carlos Hernández Garciadiego, Elena de Oteyza (1982)

Revista Matemática Hispanoamericana

Sea H un espacio de Hilbert complejo, separable y de dimensión infinita. Denotaremos por L(H) al álgebra de todos los operadores acotados en H. Carl Pearcy en 1977 introdujo el concepto de figura espectral de un operador T en L(H) [13]. Sin lugar a dudas hay dos resultados que hacen de la figura espectral de un operador un concepto importante. El primero se debe a Brown, Douglas y Fillmore:"Dos operadores esencialmente normales son débilmente equivalentes si y sólo si tienen la misma figura espectral".El...

La g -fonction de Littlewood-Paley associée à un opérateur différentiel singulier sur ( 0 , )

A. Achour, K. Trimeche (1983)

Annales de l'institut Fourier

Dans son livre [H. Stein, Ann. of Math. Studies, 63, Princeton Univ. Press, (1970)] E. Stein associe à tout opérateur de Sturm-Liouville la g -fonction de Littlewood-Paley et conjecture que, pour tout p dans l’intervalle ] 1 , [ , il existe deux constantes C p et D p telles que : C p f p g ( f ) p D p f p . On démontre ces inégalités pour une classe d’opérateurs différentiels singuliers sur ] 0 , [ et on énonce alors un résultat sur les multiplicateurs concernant ces opérateurs.

Lambert multipliers between L p spaces

M. R. Jabbarzadeh, S. Khalil Sarbaz (2010)

Czechoslovak Mathematical Journal

In this paper Lambert multipliers acting between L p spaces are characterized by using some properties of conditional expectation operator. Also, Fredholmness of corresponding bounded operators is investigated.

Lanczos-like algorithm for the time-ordered exponential: The * -inverse problem

Pierre-Louis Giscard, Stefano Pozza (2020)

Applications of Mathematics

The time-ordered exponential of a time-dependent matrix 𝖠 ( t ) is defined as the function of 𝖠 ( t ) that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in 𝖠 ( t ) . The authors have recently proposed the first Lanczos-like algorithm capable of evaluating this function. This algorithm relies on inverses of time-dependent functions with respect to a non-commutative convolution-like product, denoted by * . Yet, the existence of such inverses, crucial to...

Laplace transform identities for diffusions, with applications to rebates and barrier options

Hardy Hulley, Eckhard Platen (2008)

Banach Center Publications

We start with a general time-homogeneous scalar diffusion whose state space is an interval I ⊆ ℝ. If it is started at x ∈ I, then we consider the problem of imposing upper and/or lower boundary conditions at two points a,b ∈ I, where a < x < b. Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms...

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