 About 3,400 results  books.google.com Logarithmically subharmonic functions A notion of logarithmically subharmonic
function is rather useful. Definition. A nonnegative function u(z) is called
logarithmically subharmonic if the function v(z) = logu(z) is subharmonic. For
example, if ... 

 books.google.com (c) If u(x) is a subharmonic function, e*W is also subharmonic. This property,
which is a special case of (b), may be given a slightly different formulation if we
introduce the concept of logarithmically subharmonic function. Definition. 

 books.google.com The Newton potential and logarithmic potential of nonnegative masses, when
written with a minus sign, are subharmonic functions everywhere in the space R".
On the other hand, one of the basic theorems in the theory of subharmonic ... 

 books.google.com For £ e U, let THEOREM B. The function f » log/ig(f) is subharmonic on U [4].(')
This theorem was applied by J. Wermer to investigating the existence of analytic
discs in certain open subsets of polynomially convex sets in C2. Later on, a ... 

 books.google.com 9' Let us show now that the right member of Eq. (22) is a subharmonic function in
the domain 0'. ... function 11(2) is said to be logarithmically subharmonic in a
domain 0 if the function in u(z) is subharmonic in G. On the basis of section 9.11,
... 

 books.google.com A)"1s, for a fixed vector g the logarithm of the norm of the resolvent log (C/ — .A
)1 does not necessarily have ... If log W(£, ry) is a subharmonic function, then W
(£, 77) is said to be logarithmically subharmonic. REMARK 13.7.2. One can ... 

 books.google.com If E is a measurable set of logarithmic measure m × 60, we can include E in an
open set G of logarithmic measure less ... we mainly investigate the limiting
behaviour of a subharmonic function u(z) in a domain G as z approaches the
boundary ... 

 books.google.com In other words, (X(z) is a logarithmic subharmonic function. It is known that a
finite sum of logarithmic subharmonic functions is a logarithmic subharmonic
function, i.e. log (2^. q \Q j (z) 2) is subharmonic. But then the upper envelope of
this ... 

 books.google.com The reason is that being logarithmically subharmonic and being logarithmically
superharmonic are both local properties. This makes it plausible that being an
interpolation family might be equivalent to having the norm function satisfy a ... 

 books.google.com functions fJ(z) are holomorphic in some domain D C C'; and that A C D C {[23 <ri,
i: 1, ~ ~ ~ , n}, where ri are certain positive ... Let points 2%) be in s “For the
definition of logarithmically subharmonic functions, see I. I. Privalov,
Subharmonic ... 

 