Results 1 to 10 of about 11,357 (198)
Pseudodifferential operators with homogeneous symbols.
Michigan Mathematical Journal, 1999 The authors define homogeneous symbols as symbols \(a(x,\xi)\) in \(C^\infty(\mathbb{R}^n\times (\mathbb{R}^n/0))\) satisfying \[ |D^\alpha_x D^\beta_\xi a(x,\xi)|\leq C_{\alpha\beta}|\xi|^{m- |\beta|+|\alpha|} \] for all \(\alpha\), \(\beta\), with constants \(C_{\alpha\beta}\) independent of \(x\in\mathbb{R}^n\), \(\xi\in \mathbb{R}^n/0\).
Grafakos, Loukas, Torres, Rodolfo H.
openaire +2 more sources
Almost Diagonalization of Pseudodifferential Operators [PDF]
, 2019 In this review we focus on the almost diagonalization of pseudodifferential operators and highlight the advantages that time-frequency techniques provide here. In particular, we retrace the steps of an insightful paper by Gr chenig, who succeeded in characterizing a class of symbols previously investigated by Se strand by noticing that Gabor frames ...
openaire +2 more sources
Fundamental Results for Pseudo-Differential Operators of Type 1, 1
Axioms, 2016 This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type 1 , 1 in Hörmander’s sense. Thus, it contributes to the long-standing problem of creating
Jon Johnsen
doaj +1 more source
MathematicsWe describe the Friedrichs extension of elliptic symmetric pseudodifferential operators on a closed smooth manifold with the domain consisting of functions vanishing on a given submanifold.
Anton Savin
doaj +1 more source
Families Index for Pseudodifferential Operators on Manifolds with Boundary
, 2003 An analytic index is defined for a family of cusp pseudodifferential operators, $P_b,$ on a fibration with fibres which are compact manifolds with boundaries, provided the family is elliptic and has invertible indicial family at the boundary.
Melrose, Richard, Rochon, Frederic
core +1 more source
On the Single Layer Boundary Integral Operator for the Dirac Equation. [PDF]
Complex Anal Oper Theory, 2023 Holzmann M.
europepmc +1 more source
$L^{p}$ estimates for joint quasimodes of semiclassical pseudodifferential operators
, 2018 We develop a set of $L^{p}$ estimates for functions $u$ that are a joint quasimode (approximate eigenfunction) of $r$ pseudodifferential operators $p_{1}(x,hD),\dots,p_{r}(x,hD)$. This work extends Sarnak and Marshall's work on symmetric space to cover a
Tacy, Melissa
core
Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces
Abstract and Applied Analysis, 2011 The authors study the boundedness for a large class of sublinear operator T generated by Calderón-Zygmund operator on generalized Morrey spaces Mp,φ.
Vagif S. Guliyev +2 more
doaj +1 more source
On a Class of h-Fourier Integral Operators
Demonstratio Mathematica, 2014 In this paper, we study the L2-boundedness and L2-compactness of a class of h-Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to 0).
Harrat Chahrazed +1 more
doaj +1 more source
The perturbed Maxwell operator as pseudodifferential operator
Documenta Mathematica, 2014 As a first step to deriving effective dynamics and ray optics, we prove that the perturbed periodic Maxwell operator in d = 3 can be seen as a pseudodifferential operator. This necessitates a better understanding of the periodic Maxwell operator
De Nittis, Giuseppe, Lein, Max
openaire +2 more sources