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Linear Fractional PDE, Uniqueness of Global Solutions

Schäfer, Ingo, Kempfle, Siegmar, Nolte, Bodo (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 47A60, 30C15.In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.

Linear Kierst-Szpilrajn theorems

L. Bernal-González (2005)

Studia Mathematica

We prove the following result which extends in a somewhat "linear" sense a theorem by Kierst and Szpilrajn and which holds on many "natural" spaces of holomorphic functions in the open unit disk 𝔻: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in 𝔻 whose domain of holomorphy is 𝔻 except for the null function. The existence of a dense linear manifold of noncontinuable functions is also shown in any domain for its full space of holomorphic...

Linear relations between modular forms for Г 0 + (p)

SoYoung Choi, Chang Heon Kim (2015)

Open Mathematics

We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.

Linearly invariant families of holomorphic functions in the unit polydisc

Janusz Godula, Victor Starkov (1996)

Banach Center Publications

In this paper we extend the definition of the linearly invariant family and the definition of the universal linearly invariant family to higher dimensional case. We characterize these classes and give some of their properties. We also give a relationship of these families with the Bloch space.

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