Fundamental solutions of singular differential equations with a bessel D B operator

Formulas for the solution of the Cauchy problem for a singular wave equation with Bessel time operator

“…We see that the measure f intro (4). Then (10) Note that relation (10) with |γ| = 0 and |β| = 0 trans forms into Asgeirsson's classical relation for the classi cal ultrahyperbolic equation (i.e., for Eq. (3) in which the Bessel operators are replaced by second deriva tives).…”

“…Consider the singular differential equation 2 It is known to the authors that, in 1991, Kipriyanov was aware of relation (10) for upper spherical means in the case n = 1.…”

$p$-capacity with Bessel convolution

“…For instance fundamental solutions are given, see e.g. [12] and [13]. Harmonic analysis associated with Bessel operator is examined, see e.g.…”

“…We begin this section by introducing some additional notation. According to (13) G a,ν * a g p,a ≤ g p,a .…”

“…In a series of works the authors pointed out that Bessel translation and convolution methods are effective tools to handle Bessel-type partial differential operators, see e.g. [16], [12], [18], [13]. It also proved useful for deriving Nikol'skii type inequality, see [4], and for giving compactness criteria in some Banach spaces, see [11].…”