The Kramers-Kronig Relations connect the real and imaginary parts of any complex-valued function that is analytic in the upper half of the complex plane, expressing each part as a specific integral transform, a Hilbert transform, of the other. Named for Hendrik Kramers and Ralph Kronig, they apply to any physical response function that respects causality, such as a material's frequency-dependent optical or electrical response, and let one part of the response be recovered entirely from a full knowledge of the other.
Facts
StatementThe real and imaginary parts of a complex function analytic in the upper half-plane are related by Hilbert transforms of each other. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Source Wolfram MathWorld: Kramers-Kronig Relations
Sources
1. Kramers-Kronig relations (Wikipedia)
FormulationQuote, Formulation
the real and imaginary parts of any complex function that is analytic in the upper half-plane
Wolfram MathWorld: Kramers-Kronig Relations
Wolfram MathWorldIn Branch: Analysis, Subject classificationsQuote, In Branch: Analysis, Subject classifications
Calculus and Analysis Integral Transforms
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.