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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
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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.
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[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
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[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
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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.
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[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
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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.
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[5] Structure in simplexes
Edward G. Effros University of Aarhus, Denmark
TBD mathscidoc:1701.331314
Acta Mathematica, 117, (1), 103-121, 1966.2
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[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
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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.
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[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
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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.
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[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
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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.
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[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
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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.
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[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
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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.
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Impact Factor
3.719
Available
1882 - 2016
Volumes
228
Issues
301
Articles
2167