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Wave front set for positive operators and for positive elements in non-commutative convolution algebras

Joachim Toft (2007)

Studia Mathematica

Let WF⁎ be the wave front set with respect to $C^{\infty}$ , quasi analyticity or analyticity, and let K be the kernel of a positive operator from $C ₀^{\infty}$ to ’. We prove that if ξ ≠ 0 and (x,x,ξ,-ξ) ∉ WF⁎(K), then (x,y,ξ,-η) ∉ WF⁎(K) and (y,x,η,-ξ) ∉ WF⁎(K) for any y,η. We apply this property to positive elements with respect to the weighted convolution $u *_{B} φ (x) = \int u (x - y) φ (y) B (x, y) d y$ , where $B \in C^{\infty}$ is appropriate, and prove that if $(u *_{B} φ, φ) \geq 0$ for every $φ \in C ₀^{\infty}$ and (0,ξ) ∉ WF⁎(u), then (x,ξ) ∉ WF⁎(u) for any x.

Wave packets techniques

Nicolas Lerner (1996/1997)

Séminaire Équations aux dérivées partielles

Weak Bloch property and weight estimates for elliptic operators

M. A. Shubin (1989/1990)

Séminaire Équations aux dérivées partielles (Polytechnique)

Weighted estimates for commutators of linear operators

Josefina Alvarez, Richard Bagby, Douglas Kurtz, Carlos Pérez (1993)

Studia Mathematica

We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted $L^{p}$ spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.

Weighted local Orlicz-Hardy spaces with applications to pseudo-differential operators [Book]

Dachun Yang, Sibei Yang (2011)

Weighted Parabolic Triebel Spaces of Product Type: Fourier Multipliers and Pseudo-Differential Operators.

Jürgen Marschall (1991)

Forum mathematicum

Weyl asymptotics for non-self-adjoint operators with small multiplicative random perturbations

Johannes Sjöstrand (2007/2008)

Séminaire Équations aux dérivées partielles

We study the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random multiplicative perturbations in arbitrary dimension. We were led to quite essential improvements of many of the probabilistic aspects.

Weyl formula for quasi-elliptic pseudo-differential operators

F. Nicola (2001)

Rendiconti del Seminario Matematico della Università di Padova

Weyl product algebras and classical modulation spaces

Anders Holst, Joachim Toft, Patrik Wahlberg (2010)

Banach Center Publications

We discuss continuity properties of the Weyl product when acting on classical modulation spaces. In particular, we prove that $M^{p, q}$ is an algebra under the Weyl product when p ∈ [1,∞] and 1 ≤ q ≤ min(p,p’).

Weyl transforms associated with the Riemann-Liouville operator.

Hamadi, N.B., Rachdi, L.T. (2006)

International Journal of Mathematics and Mathematical Sciences

When is a pseudo-differential equation solvable ?

Nicolas Lerner (2000)

Annales de l'institut Fourier

This paper begins with a broad survey of the state of the art in matters of solvability for differential and pseudo-differential equations. Then we proceed with a Hilbertian lemma which we use to prove a new solvability result.

Wiener type algebras of pseudodifferential operators

J. Sjöstrand (1994/1995)

Séminaire Équations aux dérivées partielles (Polytechnique)

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