On a differentiable map commuting with an elliptic pseudo-differential operator
نویسندگان
چکیده
منابع مشابه
On the asymptotic eigenvalue distribution of a pseudo-differential operator.
A description of the number N(K) of eigenvalues less than K for a pseudo-differential operator with positive symbol is given in terms of the number of unit cubes canonically imbedded in the subset of phase space where the symbol is less than CK. This gives back in particular the order of magnitude of N(K) for elliptic symbols.
متن کاملOn the Symbol of a Pseudo-differential Operator
In [ l ] Hörmander defines the generalized symbol of a pseudodifferential operator P as a sequence of partially defined maps between function spaces. Our purpose here is to comment on the existence of characteristic polynomial type symbols <r(P) and to obtain their composition by introducing a product structure on suitable jet bundles. In particular, this gives the lower order symbol for differ...
متن کاملMaximal operator for pseudo-differential operators with homogeneous symbols
The aim of the present paper is to obtain a Sjölin-type maximal estimate for pseudo-differential operators with homogeneous symbols. The crux of the proof is to obtain a phase decomposition formula which does not involve the time traslation. The proof is somehow parallel to the paper by Pramanik and Terwilleger (P. Malabika and E. Terwilleger, A weak L2 estimate for a maximal dyadic sum operato...
متن کاملExistence of at least three weak solutions for a quasilinear elliptic system
In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...
متن کاملOn Commuting Differential Operators
The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In this paper this relationship is explored ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1984
ISSN: 2156-2261
DOI: 10.1215/kjm/1250521393