Fonctions de mailles et théorie elliptique des opérateurs aux différences finies (suite)
Fonctions de mailles et théorie elliptique des opérateurs aux différences finies
Fourier intégraux à phases complexes
Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group
The sub-Laplacian on the Heisenberg group is first decomposed into twisted Laplacians parametrized by Planck's constant. Using Fourier-Wigner transforms so parametrized, we prove that the twisted Laplacians are globally hypoelliptic in the setting of tempered distributions. This result on global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian on the Heisenberg group.
Fractional integrals on spaces of homogeneous type
Fractional integration on the space and its dual
Fractional integrodifferentiation in Hölder classes of arbitrary order.
Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces
In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels [...] TΩ,αA1,A2,…,Ak, which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators [...] TΩ,αA1,A2,…,Ak, from [...] Mp,φ1wptoMp,φ2wq for 1 < p < q < ∞. In all cases the conditions for...
Fractional powers of closed operators
Fredholmness of pseudo-differential operators with nonregular symbols
We establish the Fredholmness of a pseudo-differential operator whose symbol is of class , , in the spatial variable. Our work here refines the work of H. Abels, C. Pfeuffer (2020).
Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces [Book]
Functional calculi for pseudodifferential operators, III
Functional Equations and Linear Transformations. IV. Interpolation.
Functional equations and linear transformations - permutability and inversion. (Short Communication).
Fundamental solutions for Dirac-type operators
We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces and . Further, we consider the Cauchy problem for this operator.
Gantmacher–Kreĭn theorem for 2 nonnegative operators in spaces of functions.
Generalizations of Melin's inequality to systems
We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.
Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch....
Generalized eigenfunctions of relativistic Schrödinger operators. I.
Geometric proofs of composition theorems for generalized Fourier integral operators.