For each p > 0 we provide the construction of a harmonic function on a homogeneous isotropic tree T in the Bergman space A(p) (sigma) with no finite radial limits anywhere. Here, sigma is an analogue of the Lebesgue measure on the tree. With the appropriate modifications, the construction yields a function in A(1) (sigma) when T is a rooted radial tree such that the number of forward neighbors increases so slowly that their reciprocals are not summable.

Cohen, J., Colonna, F., Picardello, A., & Singman, D. (2018). Fractal functions with no radial limits in Bergman spaces on trees. HOKKAIDO MATHEMATICAL JOURNAL, 47(2), 269-289.

Fractal functions with no radial limits in Bergman spaces on trees

Picardello, AM;
2018

Abstract

For each p > 0 we provide the construction of a harmonic function on a homogeneous isotropic tree T in the Bergman space A(p) (sigma) with no finite radial limits anywhere. Here, sigma is an analogue of the Lebesgue measure on the tree. With the appropriate modifications, the construction yields a function in A(1) (sigma) when T is a rooted radial tree such that the number of forward neighbors increases so slowly that their reciprocals are not summable.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
eng
Bergman space; homogeneous tree; harmonic function; radial tree
Cohen, J., Colonna, F., Picardello, A., & Singman, D. (2018). Fractal functions with no radial limits in Bergman spaces on trees. HOKKAIDO MATHEMATICAL JOURNAL, 47(2), 269-289.
Cohen, J; Colonna, F; Picardello, A; Singman, D
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/207684
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