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Sums of an entire function in certain weighted L2-spaces.

Bruno Brive (2003)

Publicacions Matemàtiques

We consider the functional equation f(z+σ) - f(z) = g(z) where σ is a complex number, f and g are entire functions of a complex variable z, with growth conditions. We prove the existence of certain types of solutions of this equation by an a priori estimate method in certain weighted L2-spaces.

Supercomplex structures, surface soliton equations, and quasiconformal mappings

Julian Ławrynowicz, Katarzyna Kędzia, Osamu Suzuki (1991)

Annales Polonici Mathematici

Hurwitz pairs and triples are discussed in connection with algebra, complex analysis, and field theory. The following results are obtained: (i) A field operator of Dirac type, which is called a Hurwitz operator, is introduced by use of a Hurwitz pair and its characterization is given (Theorem 1). (ii) A field equation of the elliptic Neveu-Schwarz model of superstring theory is obtained from the Hurwitz pair (⁴,³) (Theorem 2), and its counterpart connected with the Hurwitz triple ( 11 , 11 , 26 ) is mentioned....

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