Harmonic function theory. 2nd ed.

*(English)*Zbl 0959.31001Graduate Texts in Mathematics. 137. New York, NY: Springer. xi, 259 p. DM 119.00; öS 869.00; sFr. 103.00; £41.00; $ 49.95 (2001).

This is a new edition of a nice textbook (for a review of the 1st ed. (Springer 1992) see Zbl 0765.31001) on harmonic functions in Euclidean spaces, suitable for a beginning graduate level course. A chapter on harmonic polynomials and spherical harmonics is completely rewritten, the treatment of the subject being considerably simplified.

Some new material is included: a formula for the Laplacian of the Kelvin transform; solvability of the Dirichlet problem for a half-space with continuous data; recent results on Bôcher’s theorem. New exercises are added and numerous minor improvements throughout the text are made.

Reviewer: Alexander Yu.Rashkovsky (Khar’kov)

##### MSC:

31-01 | Textbooks (potential theory) |

31B05 | Harmonic, subharmonic, superharmonic functions (higher-dimensional) |

31-04 | Machine computation, programs (potential theory) |

31C05 | Generalizations of harmonic (subharmonic, superharmonic) functions |