Pseudo differential operators with negative definite symbols of variable order

By Walter Hoh. 2000

60 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5c5b99af919fbbd7dd5ce209fd2ef38531c101a0

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In Artificial Intelligence

Citations in the corpus

Cauchy and Nonlocal Multi-Point Problems for Distributed Order Pseudo-Differential Equations, Part One (2005, background): “For more general operators on the right hand side of (7), including operators with variable orders, the corresponding Feller semigroups are constructed in [18]– [21].”
Levy-Type Processes and Pseudodifferential Operators (2001, methodology): “Symbols of variable order of differentiation were examined by various authors, among them Hoh [51], Kikuchi and Negoro [76], Negoro [91], Tsuchiya [134], Uemura [135], and [69].”
Besov spaces with variable smoothness and integrability (2010, methodology): “For further considerations of ΨDEs, we refer to Hoh [22] and references therein.”
Random Fractals and Markov Processes (2005, unknown): “Its symbol is of the form q(x, ξ) = |ξ|α(x) or q(x, ξ) ³ 1 + |ξ|α(x), where the function α(x) satisfies 0 < α0 ≤ α(x) ≤ α∞ < 2 and has modulus of continuity of order o(| log h|−1) as h → 0; cf. Bass (1988a, b), Hoh (2000), Kikuchi and Negoro (1997).”
Mixed local and nonlocal elliptic operators: regularity and maximum principles (2020, background): “Though conceptually different, the problems related to mixed order equations are closely related in spirit to the ones of variable order equations (see [34, 7, 8, 41]), which have themselves concrete significance in applied sciences (see e.”
Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order (2005, background): “Under rather strong smoothness assumptions on the measure n x dh generators of jump processes that are anisotropic or of variable order have been studied in Jacob and Leopold (1993), Hoh (1994, 2000), and Kolokoltsov (2000).”