Causal (anticausal) Bessel derivative and the ultrahyperbolic Bessel operator

• Main Authors: Manuel Aguirre Téllez, Rubén Alejandro Cerutti
• Format: Article
• Language: English
• Published: Università degli Studi di Catania 1997-11-01
• Series: Le Matematiche
• Online Access: http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/413

Let<em> B^α_C</em> and<em> B^α_A</em> be ultrahyperbolic Bessel operator causal (anticausal) of the order α defined by<em> B^α_C</em> f <em>= G_α ( P + i0, m, n) ∗ f , B^α f = G_α ( P −i0, m, n) ∗ f and let D^α_C and D^α_A</em> be generalized causal (anticausal) Bessel derivative of order α defined by <em>D^α_C f = G_{−α} ( P − i0, m, n) ∗ f , D^α_A f =G_{−α} ( P + i0, m, n) ∗ f</em> . In this note we give a sense to several relations of type:<br />                             <em> B^α_C (B^β_ A f ) + B^α_A (B^β_C f ),</em><br /><br />                              <em> D^ α_C (D^β_ A f ) + D^α_A (D^β_C f ),</em><br />                               <br />                                              .  .  .<br />