A rank theorem for analytic maps between power series spaces
A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence
We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.
A reduction method for proving the existence of solutions to elliptic equations involving the -Laplacian.
A Reduction Theorem for Cohomology Groups of Very Strongly q-convex Kähler Manifolds.
A regularity lemma for functions of several variables.
We shall prove the following Theorem. Let Fs and Fu be two continuous transverse foliations with uniformly smooth leaves, of some manifold. If f is uniformly smooth along the leaves of Fs and Fu, then f is smooth.
A regularity theorem for harmonic mappings.
A Relation Between Growth and the Spectrum of the Laplacian.
A relationship between volume, injectivity radius, and eigenvalues.
A Remark on H1 Mappings.
A Remark on Invariant Pseudo-Differential Operators.
A Remark on Lefschetz Formulae for Modest Vector Bundles.
A remark on linear functions on the sphere
A remark on multiplicity of solutions for the Ginzburg-Landau equation
A remark on natural quantum Lagrangians and natural generalized Schrödinger operators in Galilei quantum mechanics
A remark on small divisors problems
A remark on the bifurcation diagrams of superlinear elliptic equations
We prove a formula relating the index of a solution and the rotation number of a certain complex vector along bifurcation diagrams.
A remark on the differential equations on the sphere
A remark on the local Lipschitz continuity of vector hysteresis operators
It is known that the vector stop operator with a convex closed characteristic of class is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping is Lipschitz continuous on the boundary of . We prove that in the regular case, this condition is also necessary.
A representation of the coalgebra of derivations for smooth spaces
Let be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra for any positive integer . This is spanned over by , and has comultiplication and counit defined by and (Kronecker’s delta) for any . This note presents a representation of the coalgebra by using smooth spaces and a procedure of microlocalization. The author gives an interpretation of this result following the principles of the quantum theory of geometric spaces.
A representation of the space ... (K).