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

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).

Logarithmic Sobolev Spaces and Their Applications to Spectral Theory

1995 ◽  
Vol s3-71 (2) ◽  
pp. 333-371 ◽  
Author(s):  
D. E. Edmunds ◽  
H. Triebel
Keyword(s):  
Spectral Theory ◽  
Sobolev Spaces

scholarly journals Pseudodifferential calculus on noncommutative tori, II. Main properties

2019 ◽  
Vol 30 (08) ◽  
pp. 1950034 ◽  
Author(s):  
Hyunsu Ha ◽  
Gihyun Lee ◽  
Raphaël Ponge
Keyword(s):  
Spectral Theory ◽  
Trace Formula ◽  
Sobolev Spaces ◽  
Pseudodifferential Operators ◽  
Elliptic Operators ◽  
Schatten Class ◽  
Noncommutative Tori ◽  
Dimension Formula ◽  
Pseudodifferential Calculus ◽  
Negative Order

This paper is the second part of a two-paper series whose aim is to give a detailed description of Connes’ pseudodifferential calculus on noncommutative [Formula: see text]-tori, [Formula: see text]. We make use of the tools introduced in the 1st part to deal with the main properties of pseudodifferential operators on noncommutative tori of any dimension [Formula: see text]. This includes the main results mentioned in [2, 5, 11]. We also obtain further results regarding action on Sobolev spaces, spectral theory of elliptic operators, and Schatten-class properties of pseudodifferential operators of negative order, including a trace-formula for pseudodifferential operators of order [Formula: see text].

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
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