MathSciDoc: An Archive for Mathematician ∫
- Home
-
Mathematics
-
- All
- Algebraic Geometry
- Arithmetic Geometry and Commutative Algebra
- Combinatorics
- Convex and Discrete Geometry
- Differential Geometry
- Functional Analysis
- Geometric Analysis and Geometric Topology
- History and Overview
- Logic
- Metric Geometry
- Numerical Linear Algebra
- Probability
- Rings and Algebras
- Statistics Theory and Methods，Data Analysis
- Theoretical Physics
- Lecture Notes
- All
- Algebraic Topology and General Topology
- Category Theory
- Complex Variables and Complex Analysis
- Data Analysis
- Dynamical Systems
- General Mathematics
- Geometric Modeling and Processing
- Information Theory
- Machine Learning
- Number Theory
- Numerical comparisons based on four smoothing functions for absolute value equation
- Quantum Algebra
- Spectral Theory and Operator Algebra
- Symplectic Geometry
- All
- Publications of CMSA of Harvard
- All
- Analysis of PDEs
- Classical Analysis and ODEs
- Computational Geometry
- Data Analysis, Bio-Statistics, Bio-Mathematics
- Fluid Dynamics and Shock Waves
- General Methematics
- Group Theory and Lie Theory
- K-Theory and Homology
- Mathematical Physics
- Numerical Analysis and Scientific Computing
- Optimization and Control
- Representation Theory
- Statistics Theory and Methods
- TBD
- All
- S.-T. Yau High School Science Awarded Papers
-
- Journal
- Call For Papers
- Awarded Papers
- Videos
Acta Mathematica, 1996, Volume 117
ISSN:
0001-5962 (Print)
1871-2509 (Online)
In this volume (10 articles)
Issue 1
[1] On entire functions of exponential type and indicators of analytic functionals
C. O. Kiselman The University of Stockholm, Stockholm, Sweden
TBD mathscidoc:1701.331310
Acta Mathematica, 117, (1), 1-35, 1966.5
[ Download
]
[ 2017-01-08 20:32:09 uploaded by
actaadmin
]
[ 994 downloads ]
[ 0 comments
]
[ Cited by 40 ]
[ Abstract ]
[ Full ]
Citation
1
Kiselman C O. The partial Legendre transformation for plurisubharmonic functions[J]. Inventiones Mathematicae, 1978, 49(2): 137-148.
2
Berenstein C A, Struppa D C. Complex Analysis and Convolution Equations[C]., 1993: 1-108.
3
Siu Y. Pseudoconvexity and the problem of Levi[J]. Bulletin of the American Mathematical Society, 1978, 84(4): 481-512.
4
Krivosheev A S, Napalkov V V. Complex analysis and convolution operators[J]. Russian Mathematical Surveys, 1992, 47(6): 1-56.
5
Nachbin L. Recent developments in infinite dimensional holomorphy[J]. Bulletin of the American Mathematical Society, 1973, 79(4): 625-640.
6
Berenstein C A, Dostal M A. The Ritt theorem in several variables[J]. Arkiv för Matematik, 1974: 267-280.
7
Hirschowitz A. Pseudoconvexit au-dessus d\u0027espaces plus ou moins homognes[J]. Inventiones Mathematicae, 1974, 26(4): 303-322.
8
Mats Neymark. On the laplace transform of functionals on classes of infinitely differentiable functions. 1969.
9
Kiselman C O. Plurisubharmonic functions and potential theory in several complex variables[C]., 2000: 655-714.
10
Kiselman C O. Tangents of plurisubharmonic functions[C]., 1988.
Abstract
We shall be concerned with the indicator$p$of an analytic functional μ on a complex manifold$U$: $$p(\varphi ) = \overline {\mathop {\lim }\limits_{t \to + \infty } } \frac{l}{t}\log \left| {\mu (e^{t\varphi } )} \right|,$$ where ϕ is an arbitrary analytic function on$U$. More specifically, we shall consider the smallest upper semicontinuous majorant$p$^{$J$}of the restriction of$p$to a subspace £ of the analytic functions. An obvious problem is then to characterize the set of functions$p$^{$J$}which can occur as regularizations of indicators. In the case when$U$=$C$^{$n$}and £ is the space of all linear functions on$C$^{$n$}, this set can be described more easily as the set of functions(0.1) $$\mathop {\lim }\limits_{\theta \to \zeta } \overline {\mathop {\lim }\limits_{t \to + \infty } } \frac{l}{t}\log \left| {u(t\theta )} \right|$$ of$n$complex variables ζ∈$C$^{$n$}where$u$is an entire function of exponential type in$C$^{$n$}. We hall prove that a function in$C$^{$n$}is of the form (0.1) for some entire function$u$of exponential type if and only if it is plurisubharmonic and positively homogeneous of order one (Theorem 3.4). The proof is based on the characterization given by Fujita and Takeuchi of those open subsets of complex projective$n$-space which are Stein manifolds.
Please log in for comment!
[2] Necessary density conditions for sampling and interpolation of certain entire functions
H. J. Landau Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey, USA
TBD mathscidoc:1701.331311
Acta Mathematica, 117, (1), 37-52, 1966.3
[ Download
]
[ 2017-01-08 20:32:09 uploaded by
actaadmin
]
[ 930 downloads ]
[ 0 comments
]
[ Cited by 193 ]
[ Abstract ]
[ Full ]
Please log in for comment!
[3] The$d$-step conjecture for polyhedra of dimension$d$<6
Victor Klee University of Washington and Boeing Scientific Research Laboratories, Seattle, Wash., USA David W. Walkup University of Washington and Boeing Scientific Research Laboratories, Seattle, Wash., USA
TBD mathscidoc:1701.331312
Acta Mathematica, 117, (1), 53-78, 1966.4
[ Download
]
[ 2017-01-08 20:32:09 uploaded by
actaadmin
]
[ 832 downloads ]
[ 0 comments
]
[ Abstract ]
[ Full ]
Abstract
Two functions Δ and Δ_{$b$}, of interest in combinatorial geometry and the theory of linear programming, are defined and studied. Δ($d, n$) is the maximum diameter of convex polyhedra of dimension$d$with$n$faces of dimension$d$−1; similarly, Δ_{$b$}($d,n$) is the maximum diameter of bounded polyhedra of dimension$d$with$n$faces of dimension$d$−1. The diameter of a polyhedron$P$is the smallest integer$l$such that any two vertices of$P$can be joined by a path of$l$or fewer edges of$P$. It is shown that the bounded$d$-step conjecture, i.e. Δ_{$b$}$(d,2d)=d$, is true for$d$≤5. It is also shown that the general$d$-step conjecture, i.e. Δ($d, 2d$)≤$d$, of significance in linear programming, is false for$d$≥4. A number of other specific values and bounds for Δ and Δ_{$b$}are presented.
Please log in for comment!
[4] Dual representations of Banach algebras
F. F. Bonsall The University, Edinburgh, Seotland J. Duncan The University, Edinburgh, Seotland
TBD mathscidoc:1701.331313
Acta Mathematica, 117, (1), 79-102, 1965.11
[ Download
]
[ 2017-01-08 20:32:10 uploaded by
actaadmin
]
[ 1195 downloads ]
[ 0 comments
]
[ Cited by 4 ]
[ Abstract ]
[ Full ]
Citation
1
Crabb M J. A new prime C∗-algebra that is not primitive[J]. Journal of Functional Analysis, 2006, 236(2): 630-633.
2
Crabb M J, Duncan J, Mcgregor C M, et al. On one-sided primitivity of Banach algebras[J]. Proceedings of The Edinburgh Mathematical Society, 2008, 53(01).
3
Filali M, Neufang M, Monfared M S, et al. Representations of Banach algebras subordinate to topologically introverted spaces[J]. Transactions of the American Mathematical Society, 2015, 367(11): 8033-8050.
4
John Duncan. Compact operators and Banach algebras. 1971.
Please log in for comment!
[5] Structure in simplexes
Edward G. Effros University of Aarhus, Denmark
TBD mathscidoc:1701.331314
Acta Mathematica, 117, (1), 103-121, 1966.2
[ Download
]
[ 2017-01-08 20:32:10 uploaded by
actaadmin
]
[ 770 downloads ]
[ 0 comments
]
[ Abstract ]
[ Full ]
Please log in for comment!
[6] The$H$^{p}spaces of a class of function algebras
P. R. ahern University of California, Los Angeles, California, USA Donald Sarason University of California, Los Angeles, California, USA
TBD mathscidoc:1701.331315
Acta Mathematica, 117, (1), 123-163, 1965.7
[ Download
]
[ 2017-01-08 20:32:10 uploaded by
actaadmin
]
[ 999 downloads ]
[ 0 comments
]
[ Cited by 3 ]
[ Abstract ]
[ Full ]
Citation
1
Li J, Pan Z. Annihilator-preserving maps, multipliers, and derivations[J]. Linear Algebra and its Applications, 2010, 432(1): 5-13.
2
Melissa Duchsherer · Benton L Duncan. Some point derivations for semicrossed products. 2014.
3
Elias G Katsoulis. Local maps and the representation theory of operator algebras. 2015.
Please log in for comment!
[7] A characterization of linearly continuous functions whose partial derivatives are measures
Casper Goffman Purdue University, Lafayette, Indiana, USA
TBD mathscidoc:1701.331316
Acta Mathematica, 117, (1), 165-190, 1966.4
[ Download
]
[ 2017-01-08 20:32:10 uploaded by
actaadmin
]
[ 898 downloads ]
[ 0 comments
]
[ Cited by 4 ]
[ Abstract ]
[ Full ]
Citation
1
Olshen R A. Tree-structured regression and the differentiation of integrals[J]. Annals of Statistics, 2007, 35(1): 1-12.
2
Ofarrell A G. An Example on Sobolev Space Approximation[J]. Bulletin of The London Mathematical Society, 1997, 29(4): 470-474.
3
William P Ziemer. The area and variation of linearly continuous functions. 1969.
4
Goffman C. Decomposition of functions whose partial derivatives are measures[J]. Mathematika, 1968, 15(02): 149-152.
Please log in for comment!
[8] The microubundle representation theorem
Per Holm The University of Oslo, Oslo, Norway
TBD mathscidoc:1701.331317
Acta Mathematica, 117, (1), 191-213, 1966.8
[ Download
]
[ 2017-01-08 20:32:10 uploaded by
actaadmin
]
[ 899 downloads ]
[ 0 comments
]
[ Cited by 4 ]
[ Abstract ]
[ Full ]
Citation
1
Derwent J. A note on numerable covers[J]. Proceedings of the American Mathematical Society, 1968, 19(5): 1130-1132.
2
Per Holm. Microbundles andS-duality. 1967.
3
Holm P. Microbundles and S -duality[J]. Acta Mathematica, 1967.
4
Jing Mei Guo. Lip Automorphism Germ and Lip Automorphism. 2004.
Please log in for comment!
[9] Symplectic representations of algebraic groups satisfying a certain analyticity condition
Ichiro Satake The University of Chicago, Chicago, Ill., USA
TBD mathscidoc:1701.331318
Acta Mathematica, 117, (1), 215-279, 1966.4
[ Download
]
[ 2017-01-08 20:32:10 uploaded by
actaadmin
]
[ 1316 downloads ]
[ 0 comments
]
[ Cited by 26 ]
[ Abstract ]
[ Full ]
Citation
1
Michio Kuga · Ichiro Satake. Abelian varieties attached to polarizedK 3-surfaces. 1967.
2
Riehm C. The Corestriction of Algebraic Structures[J]. Inventiones Mathematicae, 1970, 11(1): 73-98.
3
Tankeev S G. ON ALGEBRAIC CYCLES ON SURFACES AND ABELIAN VARIETIES[J]. Mathematics of The Ussr-izvestiya, 1982, 18(2): 349-380.
4
Adrian Vasiu. Some cases of the Mumford-Tate conjecture and Shimura varieties. 2002.
5
Milne J S. Shimura Varieties and Moduli[C]., 2011.
6
Tankeev S G. ABELIAN VARIETIES AND THE GENERAL HODGE CONJECTURE[J]. Izvestiya: Mathematics, 1994, 43(1): 179-191.
7
Vasiu A. Integral canonical models of unitary Shimura varieties[J]. Asian Journal of Mathematics, 2005, 12(2): 151-176.
8
Ichiro Satake. On a certain invariant of the groups of type $E_{6}$ and $E_{7}$. 1968.
9
Geatti L, Gorodski C. Polar orthogonal representations of real reductive algebraic groups[J]. Journal of Algebra, 2008, 320(7): 3036-3061.
10
Vasiu A. Geometry of Shimura varieties of Hodge type over finite fields[C]., 2007.
Please log in for comment!
[10] On the greatest prime factor of a quadratic polynomial
Christopher Hooley Durham University, England
TBD mathscidoc:1701.331319
Acta Mathematica, 117, (1), 281-299, 1996.5
[ Download
]
[ 2017-01-08 20:32:10 uploaded by
actaadmin
]
[ 1424 downloads ]
[ 0 comments
]
[ Cited by 21 ]
[ Abstract ]
[ Full ]
Citation
1
Iwaniec H, Deshouillers J M. Kloosterman sums and Fourier coefficients of cusp forms[J]. Inventiones Mathematicae, 1982, 70(2): 219-288.
2
Henryk Iwaniec. Almost-Primes Represented by Quadratic Polynomials.. 1978.
3
Friedlander J B, Iwaniec H. Quadratic polynomials and quadratic forms[J]. Acta Mathematica, 1978, 141(1): 1-15.
4
Pintz J. Landau\u0027s problems on primes[J]. Journal de Theorie des Nombres de Bordeaux, 2009, 21(2): 357-404.
5
Heathbrown D R. THE LARGEST PRIME FACTOR OF X 3 + 2[J]. Proceedings of The London Mathematical Society, 2001, 82(03): 554-596.
6
Christopher Hooley. On the largest prime factor of p+ a. 1973.
7
Greaves G. Large prime factors of binary forms[J]. Journal of Number Theory, 1971, 3(1): 35-59.
8
Erdiis P, Stewart C L. ON THE GREATEST AND LEAST PRIME FACTORS OF n!+l[J]. Journal of The London Mathematical Society-second Series, 1976: 513-519.
9
Heathbrown D R, Celebration K C. Arithmetic applications of Kloosterman sums[C]., 2000.
10
Baier S, Zhao L. On primes in quadratic progressions[J]. International Journal of Number Theory, 2007, 05(06): 1017-1035.
Please log in for comment!
Impact Factor
3.719
Available
1882 - 2016
Volumes
228
Issues
301
Articles
2167