| 31. | More recent background field removal methods directly or indirectly exploit the fact that the background field is a harmonic function.
|
| 32. | The definition of harmonic functions and 1-forms is intrinsic and only relies on the underlying Riemann surface structure.
|
| 33. | His works include theory of functions of complex variables, theory of approximation, and theory of potential and harmonic functions.
|
| 34. | Any smooth complex-valued function on a sphere can be written as a weighted sum of the spherical harmonic functions.
|
| 35. | Let " u " be a real harmonic function on ? extending to a smooth function on its closure.
|
| 36. | This mean value property immediately implies that a non-constant harmonic function cannot assume its maximum value at an interior point.
|
| 37. | Third, one can use conformal transforms to map harmonic functions in one disk to harmonic functions on a half-plane.
|
| 38. | Third, one can use conformal transforms to map harmonic functions in one disk to harmonic functions on a half-plane.
|
| 39. | Just as harmonic functions in 2 variables are closely related to complex analytic functions, so are biharmonic functions in 2 variables.
|
| 40. | The eigenvalue, E _ { e } ( X _ n ) is often approximated by an harmonic function for simplification.
|
