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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...

Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case

Carlota Maria Cuesta, Xuban Diez-Izagirre (2023)

Czechoslovak Mathematical Journal

We study the large time behaviour of the solutions of a nonlocal regularisation of a scalar conservation law. This regularisation is given by a fractional derivative of order 1 + α , with α ( 0 , 1 ) , which is a Riesz-Feller operator. The nonlinear flux is given by the locally Lipschitz function | u | q - 1 u / q for q > 1 . We show that in the sub-critical case, 1 < q < 1 + α , the large time behaviour is governed by the unique entropy solution of the scalar conservation law. Our proof adapts the proofs of the analogous results for the local...

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