The analysis of linear partial differential operators

By L. Hörmander. 1990

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Citations in the corpus

Vanishing viscosity plane parallel channel flow and related singular perturbation problems (2008, background): “These works also develop a related class of pseudodifferential operators; see also [11] and [4], §18.”
Erratum for "Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions" (2002, unknown): “Given any geodesic γ in SN , there is a first order, classical, selfadjoint pseudodifferential operator Q satisfying the transmission condition (see [4], section 18.”
Enhanced dissipation and Hörmander's hypoellipticity (2021, methodology): “Hörmander’s theorem was reproved using pseudodifferential operators by Kohn in [36], and it is Kohn’s proof which Hörmander includes in his monograph [32], see Chapter 22.”
A Few Endpoint Geodesic Restriction Estimates for Eigenfunctions (2012, unknown): “Since χ̂(τ) = (2π) ( ρ̂ ∗ ρ̂ ) (τ) vanishes when |τ | is larger than half the injectivity radius of (M, g), we may use the Hadamard parametrix (see [18] and [30]) to evaluate our kernel in (2.”
Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients (2004, unknown): “[4] L. Hörmander (1985).”
Continuous curvelet transform: II. Discretization and frames (2005, unknown): “A (local) Fourier Integral Operator of order 0 [11] [8] here a belongs to the symbol class S 0 (R 4 × R 2 ) of usual pseudo-differential symbols as in [11], and the phase function Φ satisfies nondegeneracy conditions det( ∂ ∂x i ∂ ∂ξ j Φ) = 0; det( ∂ ∂y i ∂ ∂ξ j Φ) = 0.”