scholarly journals Invariant Cauchy-Riemann operators and relative discrete series of line bundles over the unit ball of C d .

1998 ◽  
Vol 45 (2) ◽  
pp. 387-397 ◽  
Author(s):  
Jaak Peetre ◽  
Genkai Zhang
1996 ◽  
Vol 46 (4) ◽  
pp. 1011-1026 ◽  
Author(s):  
Anthony H. Dooley ◽  
Bent Ørsted ◽  
Genkai Zhang

2004 ◽  
Vol 47 (1) ◽  
pp. 191-204 ◽  
Author(s):  
E. Malinnikova

AbstractLet $u$ be a solution of a generalized Cauchy–Riemann system in $\mathbb{R}^n$. Suppose that $|u|\le1$ in the unit ball and $|u|\le\varepsilon$ on some closed set $E$. Classical results say that if $E$ is a set of positive Lebesgue measure, then $|u|\le C\varepsilon^\alpha$ on any compact subset of the unit ball. In the present work the same estimate is proved provided that $E$ is a subset of a hyperplane and the (capacitary) dimension of $E$ is greater than $n-2$. The proof gives control of constants $C$ and $\alpha$.AMS 2000 Mathematics subject classification: Primary 31B35. Secondary 35B35; 35J45


2012 ◽  
Vol 262 (7) ◽  
pp. 2979-3005 ◽  
Author(s):  
Heping Liu ◽  
Genkai Zhang
Keyword(s):  

2018 ◽  
Vol 13 (4) ◽  
pp. 496-517
Author(s):  
Ned Hercock

This essay examines the objects in George Oppen's Discrete Series (1934). It considers their primary property to be their hardness – many of them have distinctively uniform and impenetrable surfaces. This hardness and uniformity is contrasted with 19th century organicism (Gerard Manley Hopkins and John Ruskin). Taking my cue from Kirsten Blythe Painter I show how in their work with hard objects these poems participate within a wider cultural and philosophical turn towards hardness in the early twentieth century (Marcel Duchamp, Adolf Loos, Ludwig Wittgenstein and others). I describe the thinking these poems do with regard to industrialization and to human experience of a resolutely object world – I argue that the presentation of these objects bears witness to the production history of the type of objects which in this era are becoming preponderant in parts of the world. Finally, I suggest that the objects’ impenetrability offers a kind of anti-aesthetic relief: perception without conception. If ‘philosophy recognizes the Concept in everything’ it is still possible, these poems show, to experience resistance to this imperious process of conceptualization. Within thinking objects (poems) these are objects which do not think.


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