A criterion for subharmonicity of a function of the spectrum
A generalization of the Phragmén-Lindelöf principle for elliptic differential equations.
A Geometric Property of Functions Harminic in a Disk.
A new class of harmonic multivalent functions defined by an integral operator.
A Note on Tolstov's Theorem on Harmonic Functions in the Plane.
A Sharp Inequality for Subharmonic Functions on Two-Dimensional Manifolds.
A sub-regularity inequality for conjugate systems on local fields
An application of subordination on harmonic function.
Angular Limits of Holomorphic Functions Which Satisfy an Integrability Condition.
Application of the subordination principle to the harmonic mappings convex in one direction with shear construction method.
Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM
We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a δ-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on δ. We apply the obtained estimates...
Asymptotic Paths for Subharmonic Functions.
Asymptotic tracts of harmonic functions. III.
Best constants for some operators associated with the Fourier and Hilbert transforms
We determine the norm in , 1 < p < ∞, of the operator , where and are respectively the cosine and sine Fourier transforms on the positive real axis, and I is the identity operator. This solves a problem posed in 1984 by M. S. Birman [Bir] which originated in scattering theory for unbounded obstacles in the plane. We also obtain the -norms of the operators aI + bH, where H is the Hilbert transform (conjugate function operator) on the circle or real line, for arbitrary real a,b. Best...
BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.
The spectral synthesis theorem for Sobolev spaces of Hedberg and Wolff [7] has been applied in combination with duality, to problems of Lq approximation by analytic and harmonic functions. In fact, such applications were one of the main motivations to consider spectral synthesis problems in the Sobolev space setting. In this paper we go the opposite way in the context of the BMO-H1 duality: we prove a BMO approximation theorem by harmonic functions and then we apply the ideas in its proof to produce...
Boundaries for left-invariant sub-elliptic operators on semidirect products of nilpotent and abelian groups.
Boundary Behavior of Subharmonic Functions on the Unit Disk
Boundary limits of Green's potentials along curves
Bounded Harmonic Functions and Positive Ricci Curvature.
Brownian motion and generalized analytic and inner functions
Let be a mapping from an open set in into , with . To say that preserves Brownian motion, up to a random change of clock, means that is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case , , such conditions signify that corresponds to an analytic function of one complex variable. We study, essentially that case , , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for , would solve...