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On holomorphic continuation of functions along boundary sections

S. A. Imomkulov, J. U. Khujamov (2005)

Mathematica Bohemica

Let D ' n - 1 be a bounded domain of Lyapunov and f ( z ' , z n ) a holomorphic function in the cylinder D = D ' × U n and continuous on D ¯ . If for each fixed a ' in some set E D ' , with positive Lebesgue measure mes E > 0 , the function f ( a ' , z n ) of z n can be continued to a function holomorphic on the whole plane with the exception of some finite number (polar set) of singularities, then f ( z ' , z n ) can be holomorphically continued to ( D ' × ) S , where S is some analytic (closed pluripolar) subset of D ' × .

On idempotent Liftings

S. Grekas (1985)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On integrability in F-spaces

Mikhail Popov (1994)

Studia Mathematica

Some usual and unusual properties of the Riemann integral for functions x : [a,b] → X where X is an F-space are investigated. In particular, a continuous integrable l p -valued function (0 < p < 1) with non-differentiable integral function is constructed. For some class of quasi-Banach spaces X it is proved that the set of all X-valued functions with zero derivative is dense in the space of all continuous functions, and for any two continuous functions x and y there is a sequence of differentiable...

Currently displaying 561 – 580 of 1085