Mathematics and Computer Science Faculty Research
http://hdl.handle.net/11214/26
Tue, 20 Mar 2018 12:18:26 GMT2018-03-20T12:18:26ZMajorization and Domination in the Bergman Space
http://hdl.handle.net/11214/200
Majorization and Domination in the Bergman Space
Richards, Kendall C.
Let f and g be functions analytic on the unit disk and let I*
denote the Bergman norm. Conditions are identified under which there exists an
absolute constant c, with 0 < c < 1, such that the relationship Ig(z)I < If(z)I
(c < IZI < 1) will imply llgll < llfli -
10.2307/2159710
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/11214/2001993-01-01T00:00:00ZTotally monotone functions with applications to the Bergman space
http://hdl.handle.net/11214/199
Totally monotone functions with applications to the Bergman space
Richards, Kendall C.
Using a theorem of S. Bernstein [1] we prove a special case of the
following maximum principle for the Bergman space conjectured by B. Koren-
blum [3]: There exists a number S e (0, 1) such that if / and g are analytic
functions on the open unit disk D with \f{z)\ < \g{z)\ on 6 < \z\ < 1 then
II/II2 < ll^lh > where || H2 is the L2 norm with respect to area measure on
D . We prove the above conjecture when either / or g is a monomial; in this
case we show that the optimal constant S is greater than or equal to l/%/3
10.2307/2154243
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/11214/1991993-01-01T00:00:00ZComparing comparisons: Infinite sums vs. partial sums
http://hdl.handle.net/11214/198
Comparing comparisons: Infinite sums vs. partial sums
Richards, Kendall C.
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/11214/1981993-01-01T00:00:00ZInequalities for zero-balanced hypergeometric functions
http://hdl.handle.net/11214/197
Inequalities for zero-balanced hypergeometric functions
Richards, Kendall C.
The authors study certain monotoneity and convexity properties of
the Gaussian hypergeometric function and those of the Euler gamma function.
10.2307/2154966
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/11214/1971995-01-01T00:00:00Z