St. Petersburg Mathematical Journal, 16. ciltAmerican Mathematical Society, 2005 |
Kitabın içinden
7 sonuçtan 1-3 arası sonuçlar
Sayfa 291
... hypoelliptic at 0 in Rn + 2 . Proof . It suffices to show that the nonlinear eigenvalue problem n Σ D2 , + ( R ( x ′′ ) ) 2 + ( P ( x ' ) − 2 ) 2 ) u = 0 = has a nontrivial solution ( z , u ) . We can look for v ( x ' ) satisfying ...
... hypoelliptic at 0 in Rn + 2 . Proof . It suffices to show that the nonlinear eigenvalue problem n Σ D2 , + ( R ( x ′′ ) ) 2 + ( P ( x ' ) − 2 ) 2 ) u = 0 = has a nontrivial solution ( z , u ) . We can look for v ( x ' ) satisfying ...
Sayfa 293
... hypoelliptic at 0 € R3 for any even m ≥ 2 and any c € R. ( b ) Let n = 2 , and let P and Q be real homogeneous polynomials of degree m≥ 2 and satisfying ( 3.9 ) . Suppose P≥0 . If m = 2 , we assume additionally that one of the above ...
... hypoelliptic at 0 € R3 for any even m ≥ 2 and any c € R. ( b ) Let n = 2 , and let P and Q be real homogeneous polynomials of degree m≥ 2 and satisfying ( 3.9 ) . Suppose P≥0 . If m = 2 , we assume additionally that one of the above ...
Sayfa 294
... hypoelliptic outside Σ ( ellipticity ) and in the neighborhood of the points of Σ such that x 0. In this case , the operator is not analytic hypoelliptic at any point ( 0 , n + 1 , In + 2 ) . ( 2 ) For n 1 , Métivier's result2 [ 12 , 14 ] ...
... hypoelliptic outside Σ ( ellipticity ) and in the neighborhood of the points of Σ such that x 0. In this case , the operator is not analytic hypoelliptic at any point ( 0 , n + 1 , In + 2 ) . ( 2 ) For n 1 , Métivier's result2 [ 12 , 14 ] ...
İçindekiler
ISOMETRIC EMBEDDINGS OF FINITEDIMENSIONAL pSPACES | 11 |
OVER THE QUATERNIONS | 104 |
1 Introduction | 117 |
Telif Hakkı | |
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analytic approximation assume asymptotic Birman BKN-equation bounded C(zIm coefficients cohomology classes compatible components constant corresponding defined denote diffeomorphism Dirac operator domain edge eigenvalues embedding English transl estimate Euler characteristic exists finite formula geodesic graph graph-manifold harmonic Hilbert space holomorphic implies inequality integral invertible isometric K₁ kernel Lemma length function linear Math matrix matrix-valued function maximal blocks meromorphic monodromy nonzero norm NPC-solution obtain oriented Painlevé equations pair paper polynomial positive potential problem proof of Theorem properties Proposition prove rational refinable function relation representation respect result Riemann-Hilbert Riemann-Hilbert problem Riemannian manifold S₁ satisfies Schrödinger operator Seifert fibered space self-affine selfadjoint selfadjoint operators singular Sobolev Sobolev spaces solution spectrum Subsection subspace supp Suppose symmetric Theorem Theorem 3.1 theory torus vector vertex vertices zero