An Introduction to Semiclassical and Microlocal Analysis

By André Martinez. 2002

629 citations recorded by the source corpus.

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Citations in the corpus

On variational approximations in quantum molecular dynamics (2004, background): “[ 11 , 15]), but apparently not on the quality of the variational approximation.”
Carleman Estimate for Elliptic Operators with Coefficients with Jumps at an Interface in Arbitrary Dimension and Application to the Null Controllability of Linear Parabolic Equations (2010, methodology): “Hence, with (2.54), (2.55) and Garding’s inequality [ 17 ,20] we obtain”
Parametrices and dispersive estimates for Schrödinger operators with variable coefficients (2008, methodology): “We note that the use of the FBI transform in the study of PDE’s has a much longer history; we refer the reader to [20], [12], [6], [17], [ 15 ] and references therein.”
On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations (2012, background): “For references on semi-classical ψDOs the reader can consult [13,42,50].”
Between classical and quantum (2005, neutral): “, Robert (1987), Dimassi & Sjöstrand (1999), and Martinez (2002).”
The Calderón problem in transversally anisotropic geometries (2013, methodology): “We refer to [30] and [47] for a general presentation in semiclassical analysis.”
Pseudospectra of semiclassical (pseudo‐) differential operators (2004, methodology): “we now recall; see [10] for the origins of the method and [20] for a recent presentation.”
Pseudo-Differential Operators in Algebras of Generalized Functions and Global Hypoellipticity (2005, background): “Let us emphasize that in Definition 4.3 the integer N is independent of α. In [4, 5] the authors consider as symbols the elements of S m �,ρ, 0 which do not depend on � . Moreover every (a� )� ∈ S m �,ρ ,f or fi xed� , can be considered as a symbol in [4, 5]. The presence of the parameter � tending ”
Injections de Sobolev probabilistes et applications (2011, background): “Appendice B Calcul h-pseudodifférentiel Nous rappelons ici les bases du calcul h-pseudo-différentiel sur M , pour lesquelles nous renvoyons à [23].”
Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction (2010, methodology): “(In general, for Semiclassical Analysis, we address the reader to Dimassi-Sjöstrand [7], Evans-Zworski [15], Ivrii [34], Martinez [40], Robert [65], Shubin [67] and Voros [71].”
Global solutions and asymptotic behavior for two dimensional gravity water waves (2013, methodology): “We refer to the books of Dimassi-Sjöstrand [33] Martinez [51] and Zworski [69].”
Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces (2011, methodology): “for u ∈ S � (R n+1 ). We shall denote the principal symbol a0 by σ( A) .W e shall use techniques of ψDO calculus in this article, such as construction of parametrices, composition formula, formula for the symbol of the adjoint operator, etc. We refer the reader to [11, 22 , 23].”