Holomorphic extensions and domains of holomorphy for general function algebras

1974 ◽  
pp. 80-91 ◽  
Author(s):  
C. E. Rickart
Keyword(s):  
General Function ◽  
Function Algebras ◽  
Domains Of Holomorphy ◽  
Holomorphic Extensions

Maximality In Function Algebras

1970 ◽  
Vol 22 (5) ◽  
pp. 1002-1004 ◽  
Author(s):  
Robert G. Blumenthal
Keyword(s):  
Metric Space ◽  
Hausdorff Space ◽  
Function Algebra ◽  
General Function ◽  
Maximal Subalgebra ◽  
Maximal Subalgebras ◽  
Disc Algebra ◽  
Function Algebras ◽  
Closed Point ◽  
Uniformly Closed

In this paper we prove that the proper Dirichlet subalgebras of the disc algebra discovered by Browder and Wermer [1] are maximal subalgebras of the disc algebra (Theorem 2). We also give an extension to general function algebras of a theorem of Rudin [4] on the existence of maximal subalgebras of C(X). Theorem 1 implies that every function algebra defined on an uncountable metric space has a maximal subalgebra.A function algebra A on X is a uniformly closed, point-separating subalgebra of C(X), containing the constants, where X is a compact Hausdorff space. If A and B are function algebras on X, A ⊂ B, A ≠ B, we say A is a maximal subalgebra of B if whenever C is a function algebra on X with A ⊂ C ⊂ B, either C = A or C = B.

scholarly journals Wick rotations in deformation quantization

2021 ◽  
pp. 2150035
Author(s):  
Philipp Schmitt ◽  
Matthias Schötz
Keyword(s):  
Analytic Functions ◽  
Star Product ◽  
Holomorphic Extension ◽  
Star Products ◽  
Formal Deformation ◽  
Space Reduction ◽  
Function Algebras ◽  
Special Cases ◽  
Complex Projective ◽  
Holomorphic Extensions

We study formal and non-formal deformation quantizations of a family of manifolds that can be obtained by phase space reduction from [Formula: see text] with the Wick star product in arbitrary signature. Two special cases of such manifolds are the complex projective space [Formula: see text] and the complex hyperbolic disc [Formula: see text]. We generalize several older results to this setting: The construction of formal star products and their explicit description by bidifferential operators, the existence of a convergent subalgebra of “polynomial” functions, and its completion to an algebra of certain analytic functions that allow an easy characterization via their holomorphic extensions. Moreover, we find an isomorphism between the non-formal deformation quantizations for different signatures, linking, e.g., the star products on [Formula: see text] and [Formula: see text]. More precisely, we describe an isomorphism between the (polynomial or analytic) function algebras that is compatible with Poisson brackets and the convergent star products. This isomorphism is essentially given by Wick rotation, i.e. holomorphic extension of analytic functions and restriction to a new domain. It is not compatible with the [Formula: see text]-involution of pointwise complex conjugation.

scholarly journals Analytic phenomena in general function algebras

1966 ◽  
Vol 18 (2) ◽  
pp. 361-377 ◽  
Author(s):  
C. E. Rickart
Keyword(s):  
General Function ◽  
Function Algebras

Holomorphic Convexity for General Function Algebras

1968 ◽  
Vol 20 ◽  
pp. 272-290 ◽  
Author(s):  
C. E. Rickart
Keyword(s):  
Analytic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
General Situation ◽  
General Function ◽  
Function Algebras ◽  
Holomorphic Convexity

In previous papers (7; 8), we have investigated certain properties of general function algebras which may be regarded as generalizations or analogues of familiar results in the theory of analytic functions of several complex variables. This investigation is continued and expanded in the present paper. The main results concern a notion of holomorphic convexity for the general situation. We also extend somewhat several of the results obtained in the earlier papers.

Prospects of Time-Resolved Photon Emission as a Debug Tool

2002 ◽  
Author(s):  
Jim Vickers ◽  
Nader Pakdaman ◽  
Steven Kasapi
Keyword(s):  
Photon Emission ◽  
Photon Counting ◽  
Signal Propagation ◽  
General Function ◽  
Hot Electron ◽  
Detector Performance ◽  
Time Resolved ◽  
Switching Event ◽  
Emission System

Abstract Dynamic hot-electron emission using time-resolved photon counting can address the long-term failure analysis and debug requirements of the semiconductor industry's advanced devices. This article identifies the detector performance parameters and components that are required to scale and keep pace with the industry's requirements. It addresses the scalability of dynamic emission with the semiconductor advanced device roadmap. It is important to understand the limitations to determining that a switching event has occurred. The article explains the criteria for event detection, which is suitable for tracking signal propagation and looking for logic or other faults in which timing is not critical. It discusses conditions for event timing, whose goal is to determine accurately when a switching event has occurred, usually for speed path analysis. One of the uses of a dynamic emission system is to identify faults by studying the emission as a general function of time.

scholarly journals Exploring Factors Associated with Functional Change and Predictors of Participation Improvement—A Two Years Follow-Up on People with Depression

2021 ◽  
Vol 18 (7) ◽  
pp. 3439
Author(s):  
Wen-Chou Chi ◽  
Chia-Feng Yen ◽  
Tsan-Hon Liou ◽  
Kwang-Hwa Chang ◽  
Hua-Fang Liao ◽  
...  
Keyword(s):  
Functional Status ◽  
Social Participation ◽  
Negative Relationship ◽  
General Function ◽  
Living Situation ◽  
Persons With Disabilities ◽  
Factors Associated ◽  
Whodas 2.0 ◽  
Household Activities

The purpose of this study is to understand the functional status distribution and to explore the factors associated with changes in functional status and social participation in people with depression using two-year follow-up data. Subjects were selected from the Taiwan Databank of Persons with Disabilities (TDPD) if they had an evaluation date between July 2012 and 31 December 2017. We used data for 1138 individuals with multiple evaluation records and who were diagnosed with depression. The WHO Disability Assessment Schedule 2.0 (WHODAS 2.0) was the primary functional status measure. Other factors selected from the TDPD included social demographic data, living situation, employment status, economic status, and educational level. The results show scores in all dimensions of the WHODAS 2.0 declined over two years, especially in the domains of cognition, household activities, social participation, and total WHODAS 2.0 score. Aging groups showed poor recovery in cognition, getting along with others, and household activities. People living in suburban areas showed poorer recovery than people living in rural and urban areas in cognition, self-care, and general function (total score of WHODAS 2.0). Employment was also strongly associated with functional recovery in household activities, social participation, and general function. The original scores for cognition and getting along with others showed a significant negative relationship with social participation improvement. Our results can be used by policy makers to provide resources and conduct investigations, and by clinicians when making rehabilitation plans.

Sign in / Sign up

Export Citation Format

Share Document