scholarly journals Spectral theory of multiplication operators on Hardy–Sobolev spaces

2018 ◽  
Vol 275 (5) ◽  
pp. 1259-1279 ◽  
Author(s):  
Guangfu Cao ◽  
Li He ◽  
Kehe Zhu
Keyword(s):  
Spectral Theory ◽  
Sobolev Spaces ◽  
Multiplication Operators

SPECTRAL THEORY AND EMBEDDINGS OF SOBOLEV SPACES

1979 ◽  
Vol 30 (4) ◽  
pp. 431-453 ◽  
Author(s):  
D. E. EDMUNDS ◽  
W. D. EVANS
Keyword(s):  
Spectral Theory ◽  
Sobolev Spaces

Spectra of Multiplication Operators in Sobolev Spaces

2009 ◽  
Vol 55 (3-4) ◽  
pp. 281-293
Author(s):  
Hannalie Brooks ◽  
Manfred Möller
Keyword(s):  
Sobolev Spaces ◽  
Multiplication Operators

Properties of Equivalent Capacities

1971 ◽  
Vol 14 (1) ◽  
pp. 5-11 ◽  
Author(s):  
R. A. Adams
Keyword(s):  
Partial Differential Equations ◽  
Euclidean Space ◽  
Sobolev Space ◽  
Differential Equations ◽  
Spectral Theory ◽  
Sobolev Spaces ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Closed Set ◽  
Shed Light

Various definitions of capacity of a subset of a domain in Euclidean space have been used in recent times to shed light on the solvability and spectral theory of elliptic partial differential equations and to establish properties of the Sobolev spaces in which these equations are studied. In this paper we consider two definitions of the capacity of a closed set E in a domain G. One of these capacities measures, roughly speaking, the amount by which the set of function in C∞(G) which vanish near E fails to be dense in the Sobolev space Wm, p(G).

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