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Morimoto M. — Introduction to Sato's hyperfunctions
Morimoto M. — Introduction to Sato's hyperfunctions



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Название: Introduction to Sato's hyperfunctions

Автор: Morimoto M.

Аннотация:

This is the English version of the original Japanese edition written in 1976. Since then the theory of hyperfunctions has evolved into a flourishing field of Algebraic Analysis and many papers and monographs have been written on this subject. By request of the American Mathematical Society, I translated my book which, I hope, still serves as an introduction to the theory of hyperfunctions. The English edition is a mathematically faithful translation of the original Japanese edition, but all the footnotes have been incorporated in the main text and many errors have been corrected. The bibliographical notes are assembled as Appendix С and the bibliography is rearranged to reflect the more recent related publications.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 273

Добавлена в каталог: 06.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$$\mathfrak{B}(u)$      45 158
$A \subset B$      9
$Exp(E')$      16
$Exp(E';K)$      18
$Exp(E';W)$      18
$S = (v \setminus \{0\} / {\mathbb R}^{+} )$      167
$T({E}_{\nu})$      200
$T({G}_{0})$      129
$\br{b}: \mathscr{A} \to {\tau}^{-1} \mathscr{A}$      171
$\Delta({z}^{0};r)$      3
$\Gamma = \tilde{\Gamma}0$      167
$\Gamma(Y;\mathscr{F})$      73
$\Gamma[S;\mathscr{F}]$      75
$\mathfrak{B}$      158
$\mathfrak{B}(M)$      214
$\mathfrak{B}[S]$      45 159
$\mathscr{A}(u \time \sqrt{-1} \Gamma)$      168
$\mathscr{C}$      198 215
$\mathscr{C}(u \time \sqrt{-1} \Gamma)$      197
$\mathscr{C}({u}_{\pm})$      182
$\mathscr{N}(S)$      11
$\overline{\partial}$-resolution      114
$\Phi$-soft sheaf      95
$\pi: V \time \sqrt{-1} {S}^{*} \rightarrow V$      183 211
$\pi: \mathscr{F} \rightarrow X$      72
$\sqrt{-1}{S}^{*} \equiv {u}_{+} \sqcup {u}_{-}$      58
$\tau: {S}_{M} X \rightarrow M$      215
$\tilde{D}(I)$      184
$\tilde{I}$      183
${A}^{*}(u \time \sqrt{-1} I)$      223
${B}^{p}(\mathfrak{W};F)$      90
${B}_{\Phi}^{p}(X;\mathfrak{F})$      85
${C}^{0}(W)$      1
${C}^{1}$ function      4
${C}^{j}(\tilde{u};I)$      200
${C}^{k,j}$      201
${C}^{p}(\mathfrak{W}, \mathfrak{W'};F)$      90
${Exp}^{b}(E';K)$      17
${E}_{\nu}$      162
${H}^{1}[A;\mathscr{O}]$      45
${H}^{1}[K;\mathscr{O}]$      28
${H}^{1}_{A}(W;\mathscr{O})$      44
${H}^{1}_{K}(W;\mathscr{O})$      25
${H}^{j}(\tilde{u};I)$      200
${H}^{p}(\mathfrac{W},\mathfrac{W'};F)$      90
${H}^{p}(\mathfrac{W};F)$      90
${H}^{p}({\Gamma}_{\Phi}(X;{\mathscr{L}}^{*}))$      86
${H}^{p}[S;\mathscr{F}]$      88
${H}^{p}[u,S;\mathscr{F}]$      106
${H}^{p}_{c}(X;\mathscr{F})$      95
${H}^{P}_{S}(X;\mathscr{F})$      87
${H}^{P}_{\Phi}(X;\mathscr{F})$      85
${h}_{k}(\xi)$      16
${I}^{\perp}$      206
${S}^{*}M$      215
${Z}^{n-1}_{0}({\mathfrak W}(E \setminus K);{\martscr O}^{(n)})$      137
${Z}^{p}({\mathfrak W};F)$      90
${Z}^{p}_{\Phi}(X;{\martscr F})$      85
${\bf{b}}_{+}$      181
${\bf{b}}_{-}$      181
${\bf{b}}_{Z}$      216
${\bf{b}}_{\Gamma}(\phi)$      169
${\Gamma}^{\perp}$      206
${\Gamma}_{S}(W;\mathscr{F})$      74
${\mathscr A}^{*}$      223
${\mathscr h}, l$      184
${\mathscr h}, l(\Gamma)$      168
${\mathscr H}^{p}(\mathscr{L}}^{*})$      84
${\mathscr{C}}_{(x, \pm \sqrt{-1} \infty)}$      182
${\mathscr{D'}}(W)$      3
${\mathscr{D'}}_{K}(W)$      2
${\mathscr{D}}(W)$      2
${\mathscr{E'}}(W)$      3
${\mathscr{E}}(W)$      2
${\mathscr{F}}(Y)$      75
${\mathscr{F}}[S]$      75
${\mathscr{N}}_{{\mathbb{R}}^{n}}(S)$      11
${\mathscr{O}}(W)$      8
${\mathscr{O}}(W)$-convex hull      112
${\mathscr{O}}_{0}(\mathbb{C} \ K)$      29
${\Phi}_{S}$      75 87
${\pi}_{*}{\mathscr C}(u)$      211
${\tilde{\Gamma}}_{j}$      163
9-lemma      259 263
Analytic, cochain      207
Analytic, continuation      112
Analytic, functional      9
Annulus      24 132
Antipodal mapping      60
Ascoli-Arzel' theorem      9
B      215
Banach space      244
Bargman-Hall-Wightman theorem      235
Barrelled      244
Bochner tubular domain theorem      169
Bogolyubov theorem      216
Bornologique      244
Boundary operator      181
Boundary value, of holomorphic function      169
Boundary value, operator      169 216
Boundary values      46
Bounded      243
Canonical (n,0)-differential form      115
Canonical bilinear form      242
Canonical embedding      46
Canonical flabby resolution      84
Canonical mappings      245 246
Cauchy inequality      5
Cauchy integral, formula      4
Cauchy integral, theorem      4
Cauchy-Hilbert transform      28 142
Cauchy-Kovalevskaya theorem      232
Cauchy-Poincare theorem      131
Cauchy-Riemann, complex      114
Cauchy-Riemann, equations      4
Cauchy-Weil, integral formula      133
Cauchy-Weil, theorem      133
Cauchy-Weil, transform      138
Center of annulus      132
Characteristic function      55
Closed graph theorem      244
Coboundary      89
Coboundary operator      89
Cofinal      246
Cohomology group      85
Cohomology group, of complex      260 264
Cohomology group, with compact support      95
Compact mapping      249
Compatibility condition      48 80
Complete Reinhardt set      6
COMPLEX      260 264
Complex, neighborhood      11
Complex, of sheaves      84
Complexification      213
Cone      167
Conormal, space      227
Conormal, sphere bundle      183 215
Conormal, vector bundle      215
Constant presheaf      77
Convex hull      184
Convex hull, in sphere      168
Convex polyhedron      183
Convex set in sphere      168 183
Convex set in sphere bundle      216
Convolution      14
Cotangent, sphere bundle      215
Cotangent, vector bundle      215
Cylindric compact set      118
de Rham theorem      99
Decomposed singular support      220
Decomposition to plane waves      229
Decreasing family      245
Decreasing family, of locally convex spaces      246
Decreasing sequence      245
Definite integral of hyperfunction      61 229
Denning function      45 161
Denning function, of analytic functional      28
Derived sheaf with support      99
Determined singular point      69
DFS space      254
Differential operator of infinite order      40 63
Dirac $\delta$-function      52 161
Dirac measure      10
Direct image      211
Directed set      245
Distinguished boundary      3
distribution      3
Dolbeault theorem      115
Domain      6
Domain, of holomorphy      111
Dual, cone      184
Dual, set      206 216
Dual, space      242
Elliptic partial differential operator      234
Entire function of exponential type      16
Epstein theorem      217
Even hyperfunction      50
Everywhere singular      113
Exact      259 263
Exact sequence      259 263
Excision theorem      88
Exponential function      15
Extended tube      235
Family of supports      75
Finite part      54
First cohomology group, with compact support      35
First cohomology group, with support in close set      44
First cohomology group, with support in K      25
fl.dim${\mathscr{F}}$      103
Flabby dimension      103
Flabby resolution      83
Flabby sheaf      81
Fourier-Borel transform      15
Fourier-Laplace transform      37
Frechet space      244
FS space      249
Fundamental theorem of microfunctions      207
Gauss kernel      67
Gelfand representation      15
General $\delta$-function      53
Germ, of holomorphic functions      12
Germ, of presheaf      79
Germ, of real analytic functions      12
Grauert theorem      160
Hahn-Banach theorem      242
Hartogs theorem      5 112
Heaviside Y-function      54
Holomorphic, differential forms      114
Holomorphic, function      4
Holomorphic, function on $u \time \sqrt{-1} \Gamma$      168
Holomorphic, functions over tangent sphere bundle      168
Holomorphic, parameter      55
Holomorphically convex      112
Homomorphism of complexes      260 264
Hyperfunction      45 158
Image      259 263
Increasing family      245
Increasing family, of locally convex spaces      246
Increasing sequence      245
Indefinite integral      51
Inductive limit      246
Inductive ordered set      81
Injective increasing sequence      251
Invariant under the Lorentz infinitesimal transformations      238
Jost point      236
Jost theorem      236
Kaneko theorem      70
Kashiwara theorem      218
Kernel      259 263
Laplace-Martineau transform      146
Leray theorem      93
LF space      252
Lie between      24 135
Linear functional      242
Linear topological space      241
Linearly convex      113
Liouville theorem      29
Local operator      63
Localization conditions      80
Locally, analytic functional      12
Locally, closed      11
Locally, convex      241
Locally, convex space      242
Logarithmically convex      8
Long Exact Sequence      85 88
Long exact sequence, of a cohomology groups of relative covering      91
Lorentz group      235
Lower semicontinuous      244
Mackey theorem      243
Mackey-Arens theorem      244
Malgrange theorem      115
Martineau Edge-of-the-Wedge theorem      218
Martineau-Harvey theorem      148
Maximal modulus principle      6
Mayer-Vietoris theorem      190
Meromorphic hyperfunction      53
Micro-analytic      58
Micro-analytic hyperfunction      221
Microfunction      182 198
Minkowski inner product      235
Mittag-Leffler theorem      32
Montel, space      244
Montel, theorem      6
Nonregularity      68
Norm      241
Normal sphere bundle      214
Normal vector bundle      214
Normed space      244
Odd hyperfunction      50
Oka theorem      14 115
Open neighborhood of locally closed set      11
Open polydisc      3
Open set, of convergence      7
Open set, of holomorphy      111
Osgood theorem      5
p-coboundary      90
p-cochain      89
P-cocycle      90
Paley-Wiener theorem      116
Paracompact space      95
Paracompactifying support      95
Patching condition      48 81
Plurisubharmonic function      113
Poincare lemma      98
Polar set      256
Polya theorem      21
Polydisc, (closed)      3
Polyhedron      141
Polynomially convex      14
Polynomially convex hull      14
Positive light cone      235
Presheaf      76
Presheaf, homomorphism      78
Presheaf, of arbitrary functions      78
Presheaf, of G-modules      77
Presheaf, of holomorphic functions      77
Presheaf, of hyperfunctions      77
Presheaf, of real analytic functions      77
Presheaf, of rings      77
Presheaf, of sections      79
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