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Twisted spherical means in annular regions in n and support theorems

Rama Rawat, R.K. Srivastava (2009)

Annales de l’institut Fourier

Let Z ( Ann ( r , R ) ) be the class of all continuous functions f on the annulus Ann ( r , R ) in n with twisted spherical mean f × μ s ( z ) = 0 , whenever z n and s > 0 satisfy the condition that the sphere S s ( z ) Ann ( r , R ) and ball B r ( 0 ) B s ( z ) . In this paper, we give a characterization for functions in Z ( Ann ( r , R ) ) in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in n which improve some of the earlier results.

Two remarks on Kähler homogeneous manifolds

Bruce Gilligan, Karl Oeljeklaus (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that every Kähler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical.

Two remarks on the Suita conjecture

Nikolai Nikolov (2015)

Annales Polonici Mathematici

It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with C 1 + ε -smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.

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