Subharmonic Excitation—Thresholds and Limits

Separately subharmonic functions and quasi-nearly subharmonic functions

First, we give the definition for quasi-nearly subharmonic functions. Second, after recalling the existing subharmonicity results of separately subharmonic functions, we give corresponding counterparts for separately quasi-nearly subharmonic functions, thus generalizing previous results of Armitage and Gardiner, of ours, of Arsove, of Avanissian, and of Lelong.

Harmonic morphisms and subharmonic functions

Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ : M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map. Similarly, if f is a subharmonic function on N which is not harmonic and such that |df | is bounded, and ...

Generalized Covering Groups and Direct Limits

Multiplication of Subharmonic Functions

We study subharmonic functions in the unit ball of R , with either a Bloch–type growth or a growth described through integral conditions involving some involutions of the ball. Considering mappings u 7→ gu between sets of functions with a prescribed growth, we study how the choice of these sets is related to the growth of the function g.

Optimal Subharmonic Entrainment

For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the actuated process. Such subharmonic synchrony, which is dynamically established when N control cycles occur for everyM cycles of a forced oscillator, is referred t...