ここにいるよ あなたがまよわぬよう あなたがさがさぬよう
Mathematics
11/20/2004
Y. A. Alpin, M. T.
Chien and L. Yeh, The numerical radius and bounds for zeros of a polynomial,
Proceedings American Mathematical Society, 131(2003), 725-730.
The numerical range
of 3x3 matrices,
Dennis S, .Keeler,
Rodman,Leiba and Ilya M.Spitkovsky
Linear Algebra and
its Application,252:115-139(1997)
11/19/2004
Cosine Products, Fourier Transforms, and
Random Sums
Kent E. Morrison,
Amer.Math.Momthly,102:716-724,1995(also arXiv:math.CA/0411380
7/21/2004
I like the following paper
Majorization, Range Inclusion, and
Factorization for Bounded Linear Operators, Proceedings of AMS
2004,S0002-9939(04)07495-7
by Bruce A.Barnes,
which is self-contained, contains new
proofs, and is an overview paper.
7/17/2004
http://www.auburn.edu/~brownj4/
Smooth
interpolation, Hölder continuity, and the Takagi -
van der Waerden function (pdf), Amer. Math.
Monthly 110 (2003), 142-147 (with G. Kozlowski).
2/23/2004
|
ARTICLE |
Karlander, Karl http://134.76.163.65/agora_docs/226368TABLE_OF_CONTENTS.html Mathematica Scandinavica , volume.80,310-312,1997 |
2/16/2004
|
13 Feb |
math.CA/0402209
Elements of harmonic analysis. Stephen Semmes. 22 pages. CA. |
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The sharp
form the strong Szegö theorem, to appear in J.
Conf. on Geometry and Spectral Theory
Click here for .pdf file Barry Simon
1/24/2004
掛谷宗一 一般函数論 付録有界関数532-557 等摸函数
Maximum Modulus
of Some Expressions of Limited Analytic Functions
Transactions of American Mathematical Society,33, 489-504(1921)
（１）Carlsonの条件(
)は
でも同じか？
（２）解析函数の実数部>0 の条件と解析函数のnorm（sup）の条件の関係？
12/28/2003
On a property of
the Fourier transform
Karlandar,Karl in Mathematica Scandinavica,
vol.80,pp.310-312
11/24/2003
Approximation on
a Disk
Wermer,J. Mathematische
Annalen
|
Vol.155,331-333(1964) 331 |
|
SOME
RESULTS ABOUT REVERSES OF CAUCHY-SCHWARZ INEQUALITY IN INNER PRODUCT SPACES
Pinkus, A., Weierstrass and
Approximation Theory, J. Approx. Theory 107 (2000), 1-66.
|
|
Forst, Wilhelm |
||
|
Forst, Wilhelm |
|
||
Neveille
Invariant
Subspaces and Lomonosov’s Theorem
Talk
slides (pdf file).
Troitsky
http://arxiv.org/find/math/1/au:+Troitsky_V/0/1/0/all/0/1
|
|
8/26/2003
JFM 49.0207.03 Mathias, M.
Über positive Fourier-Integrale. (German)
Math. Zs. 16, 103-125 (1923). Published: 1923
Integrale de Fourier et Questions qui s’y Rattachent,
T.Carleman,Upsala,1944
Cyclic
vectors and invariant subspaces for the backward shift operator
Annals de L’Institute Fourier,1970,37-76
Weak
Compactness in Certain Star-Shift Invariant Subspaces
Akeroyd,J.R.,Khavison,Dmitry,Shapiro,H.S
2002,April,2
Interpolating
Sequences for the Multipliers of the Dirichlet Space
Donald E.
Marshall and Carl Sundberg
The
Extreme Points of a Class of Functions with Positive Real Part.
Holland,Finbarr Mathematische
Annalen vol.202,pp２８５−８８(1973)
A Simple
proof for Schur’s Theorem
R.A.Kortram
Proceedings of
AMS,vol.129,no.11,page 3211-3212(2001)
The extreme
points of a class of functions with positive real part
R.A.Kortram
Bull. Belg. Math. Soc. 4,(1997),449-459
Nevalinna Pick Interpolation with
Boundary Data
Donald Sarson,
Integr.equ.oper.Theory 30（１９９８）２３１−２５０
Lectures on
Invariant Subspaces,
Henry Helson,
Academic Press(1964)
Ungleichungen für die Koeffizienten einer Potenzreihe
Szäsz,O.(1918)
Mathematische Zeitschrift, vol.1;pp.163-183
On the Uniform
Approximation to Continuous Functikons by Linear Aggregates
of Translations,
Ulrich Abel, Mathematische Annalen, 267,453-460(1984)
http://134.76.163.65/agora_docs/advanced_search.html
Nevalinna-Pick
Interpolation: The Degenerate Case
Harald Woracek
preprint for
Linear Algebra Appl., 252(1997) 141-158
A
New Characterizartion of the Unit Ball on H^2,
R.A.Kortam, 2003,Proceeding AMS
The two-by-two
spectral Nevalinna-Pick problem, J. Agler , N.J.Young 2001
|
21 Mar |
math.NT/0209393 Zeros of the alternating zeta function on the line R(s)=1.
Jonathan Sondow.
Amer. Math. Monthly 110 (2003) 435-437. NT. |
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Proc.AMS,1998,vol.126,no.5,1311-1314
Henry
Helson,2000,
The Smirnov class
on compact groups with ordered duals
Sankhya,vol 62,ser.A,Pt3,413-418
On a
new species of imaginary quantities connected with a theory of quaternions
William Roman
Hamiltonian Proceedings of
On the
sequences of analytic functions,
Paul Montel
Early days in
complex dynamics,216-217
- (with M.Sodin) The Hamburger moment problem and weighted
polynomial approximation
on discrete subsets of the real line, Journal d'Analyse Math. 76 (1998), 219-264, MR 2000g:44017.
Click to download ps file. - (with M.Sodin) Weighted polynomial approximation and the
Hamburger moment
problem, Complex Analysis and Differential Equations. Proceedings of the Marcus
Wallenberg Symposium in Honor of Matts Essén Held in
Click to download ps file.
Schur Functions and
Orthogonal Polynomials on the Unit Circle,
Fernc Pinter and Paul Nevai, 1996 preprint version,1-11
Szego Difference
Equations,Transfer Matrices and Orthogonal Polynomials on th eUnit Circle,
Leonid Golinskii and
Pal Nevai
A generic Shur
function is an inner one,
by V.Katsnelson
Riesz’s Alternatives
Let 
be a vector space and 
be an transformation from to .
Define for
integers 
subspaces 
and 
such that
and
.
Then we easily have
(
may
be 0 or 
)
(
may
be 0 or )
We have th efollowing theorem.
Theorem.1
1.
1’. 
2.
2’.
3. 
or
3’. or
Theorem2. For
finite 
,
the followings are equivalent
1.
2.
3.
4. .
Furthermore
we have 
.
Maximal Properties of the Normalized Cauchy Transform, Alexei Poltoratski
J. of
AMS,vol16,no.1,1-17
For any summable
function 
on
the unit circle T one
can define its Cauchy integral
in the unit disk D as
(1)
,
where 
is the normalized Lebesgu
measure on T. can
also be defined on T
by its non-tangential boundary values. On
e can view the Cauchy integral as an operator
in 
which sends into the boundary values of .
(2) The Cauchy
transform is unbounded for 
.
(3) The Cauchy
transform is bonded for 
in .
(4) 
also called the Cauchy integral.
(5) The Cauchy transform is bonded for in 
if
and only if 
satisfies
the 
condition,
where
is an absolutely continuous part of .
(6) 
is the generalization of the Cauchy
transform,
where
may be a singular measure.
(7)
If 
,
.
(8)
If is a singular probability measure, 
,
where 
is an inner function,
.
On the distributions of boundary values of
Cauchy integrals, Proceeding AMS,1996,124,no.8,2455-2463
Does anyone know a reference to the
following result? If A is a square matrix
with integer entries then Trace(A^p)-Trace(A) is divisible by p if p is a
prime.
This seems a nice
generalization of Fermat's Little Theorem.
It is
fairly easy to prove, so I am pretty
sure that I am not the first to have
discovered it, but I don't know a
reference.
Chris Bernhardt
|
1. |
math.CA/9810104 Polynomial
approximation in $L_p(R, d\mu)$.
I. Andrew G. Bakan.
|
p-HYPONORMALITY
IS NOT TRANSLATION-INVARIANT,
Muneo Cho
and Jun Ik Lee
Proceeding of
AMS,2002 S0002-9939(02)06865-X
k-Hyponormality
of Powers of Weighted Shifts via Schur Products,
Raul Curto and Sang
A
formula for k-hyponormality of backstep extensions of subnormal weighted shifts,
Proc.Amer.Math.Soc.129(2001)2343-2351
Real functions in
weighted Hardy spaces, PDMI preprint(16/1996)
Vladimir
V.Kapustin,1-3 (ps.gz file)
Extremal Functions
as Divisors for Kernels of Toeplitz Operators （ps）
Andreas Hartmann and Kristian
Seip
K.M.Dyakonov, Kernels of Toeplitz Operators via Bourgain’s
Factorization Theorem,
J. Functional
Analysis,170(2000)no.1,93-106
D.Hitt Invaraint
Subspaces of H2 of an Annulus,Pacific J.
Math.134(1988)no.1,101-120
Interpolating
sequences for multipliers of the Dirichlet space (ps)
Donald E. Marshall and Carl Sundberg, Preliminary Version
Proceedings of the
American Mathematical Society
Listing of recently
posted articles: http://www.ams.org/proc/0000-000-00
G. A. Edgar;
Chris Miller
Borel subrings of the reals http://www.ams.org/jourcgi/jour-getitem?pii=S0002-9939-02-06653-4
Transactions of the
American Mathematical Society
Listing of recently
posted articles: http://www.ams.org/tran/0000-000-00
D. Alpay; T. Constantinescu; A. Dijksma; J. Rovnyak
Notes on interpolation in the generalized Schur class. II. Nudel$'$man's
problem http://www.ams.org/jourcgi/jour-getitem?pii=S0002-9947-02-03148-3
A Short Course on
Spectral Theory
William Arveson
Springer GTM２０９
http://math.berkeley.edu/~arveson/
His Lecture
Notes:
Notes on measure
and integration in locally compactspaces
Transactions of the American Mathematical Society
Volume Number: 354
Issue Number: 12
Issue Posted:
Most recent issue available at: http://www.ams.org/tran/2002-354-12
**********************************************************************
Carl Sundberg
Measures induced by analytic functions and a problem of
Walter Rudin
http://www.ams.org/jourcgi/jour-getitem?pii=S0894-0347-02-00404-6
Journal of the American Mathematical Society (2002) Sep.
2000 Mathematics Subject Classification. Primary 30D50.
Nakaji, Takahiko(2002)
The Nevalinna Counting Functions for Rudin’s
Orthogonal Functions, Proceeding AMS.,S0002-9939(02)06671-6
Codimension
of polynomial subspace in L_2(R,d) for discrete
indeterminate measure .
Andrew G.Bakan,
|
|
math-ph/9906008 The
Classical Moment Problem as a Self-Adjoint Finite
Difference Operator. Barry Simon. Advances
in Math. 137 (1998) 82-203. MP. |
藤原松三郎 複素関数論（Ｉ）岩波講座 数学
新しい数学の勉強の仕方 e-learning
http://www.math.umn.edu/~leung/OnlineLectures.html
たとえば
P.D.Lax先生のレクチャ
http://chaos.mth.msu.edu:8080/ramgen/Lax/Lax-lan.rm
を聞いてみよう。このようなことをもっと発展させたいものです。
一部の人のためのものでなくすべての人に数学を・・・
http://chaos.mth.msu.edu:8080/ramgen/Atiyah-Lectures/Video/Atiyah-MC-2.rm
elementary
geometry
http://www.math.tamu.edu/~dallen/m629_02a/video.htm
the history of
math in Greek,orient
http://www.math.duke.edu/computing/broadcast.html
Geometric Unfolding of a Difference Equation
Professor Sir Christopher Zeeman
http://www.pims.math.ca/activities/dist_lect/zeeman/zeeman.html
http://www.pims.math.ca/education/2000/CtC/coxeter/
elementary=high
school level
http://www.projectmathematics.com/index.htm
physics and
object oriented language C++,java,XML and more
http://www.wlap.org/byTitle.html
only samples but
good in view
http://www.thinkwell.com/marketing/viewLecture.cfm
the brain of human being
http://mbl.katewood.com/lecture4/transcript-interview.shtml
The spectra of nonnegative integer matrices via formal power series
Ki Hang Kim; Nicholas S. Ormes; Fred W.
Roush
J. Amer. Math. Soc. 13
(2000), 773-806.
Abstract,
references and article information
Retrieve article in: PDF
DVI
TeX
PostScript
THE COUNTEREXAMPLES IN FUNCTIONAL ANALYSIS
http://www1.um.ac.ir/~moslehian/cfa/cfa.htm
Korevaar,J. (2002) A century Complex Tauberian theory,Bulletin
American Mathematical Society, July 8
Akeroyd,John R.(2002) A Note concerning the
Index of the Shift, Proceeding of American Mathematical Society, vol.130.April 11,3349-3354,
Alex,Sheldon (1994) Down with Determinant
Integrate by
t, 
,
for 
,
we have 
.
From these
inequalities, we can see that
for 
,
we have 
,
as long as each
terms converge.
In other words, 
converge.
for .
平成14年6月25日
Hindmarsh,A. Pick conditions and
analyticity, Pacific J.math.27(1968),527-531
Adamyan,V.M.; Arov,D.Z.;Krein,M.G.
(1971) Analystic properties of the Schmidt pairs of a
Hankel operator and the generalized Schur-Takagi problem, Mat.Sb.(N.S.)86(128)
34-75
Akhiezer (1930),On a minimum problem in
function theory and the number of roots of an algebraic equation inside the
unit disk,Izv.Akad.Nauk SSSR Mat.,9,1169-1189
Carleson,(1958) An interpolation
problem for bounded analytic functions, Amer.J.Math.80,921-930
Earl,J.P.(1970) On the interpolation of
bounded sequences by bounded functions, J.London Math.Soc.,(2)2,544-548
Shapiro,H.S.;Shield,A.L.(1961) On some interpolationproblems for analytic functions,
Amer.J.Math.83,513-532
Agler,Jim;McCarthy,John E.(2000),The three Point Pick
Problem on the Bidisk, New York Journal of Math.
6,227-236
Teiji Takagi (1924)
On an Algebraic
Problem Related to an Analytic Theorem of Caratheodory
and Fejer and on an Allied Theorem of Landau.
Japanese J. Math.
vol 1. 83-93
数学は社会と関係をもつべきである。
http://mmp.maths.org/
Millennium
Mathematics Project (MMP)
Millenium Prize Problem Clay Institute’s Web site
A converse to a theorem of Adamyan,
Arov and Krein
J. Agler; N. J.
Young
J. Amer. Math. Soc. 12 (1999), 305-333.
Contents of
Volume 11, Number 4
Factorization and approximation problems for matrix
functions
V. V. Peller
J. Amer. Math. Soc. 11
(1998), 751-770.
A
MONOTONICITY PROPERTY OF POWER MEANS
Volume
3, Issue 3, 2002
Welcome
to the Journal of Inequalities
in Pure and Applied
Mathematics (JIPAM)
（１）Pick の定理の証明は
Marshall,D.E.(1974) An elementary proof of Pick-Nevalinna
interpolation theorem, Michigan Math.J.,21,219-223
がわかりやすい。あと、
Takahashi Sechiko, (1989) Extension of the theorems of Caratheodory-Toeplitz-Schur
and Pick, Pacific
J.math.,vol.138,no.2,391-399
も何かある。
（２）いま、
掛谷宗一の論文を読んでいます。
|
Kakeya, Soichi |
1925 |
On Fundamental Systems of Symmetric
Functions |
Japanese Journal Mathematics |
2 |
|
69-80 |
|
|
|
Kakeya, Soichi |
1927 |
On Fundamental Systems of Symmetric
Functions II |
Japanese Journal Mathematics |
4 |
|
77-85 |
|
|
それから
|
Nakamura,Koshiro |
1927 |
On the Representation of Symmetric
Functions by Power-Sums which form the Fundamental System |
Japanese Journal Mathematics |
4 |
|
87-92 |
|
も、じつはこのページの下のほうにある
A note on lp-norms
Behrehard,Olga Katkova, Anna Vishnyakova
に引用不明となっていた掛谷宗一の論文をぼくは偶然見つけたのでした。これをドイツのBehrehard氏に
コピーを送ってあげました。偶然見つけたというのは、藤原松三郎「代数学」という１９２０年ごろの
書物を眺めていたら、たまたま、その定理が証明なしに載っているのを見つけました。
それもこれも、伊藤先生が「代数学」の行列の非負性を行列式で正確には正と負でないとの区別をしている
部分をコピーしてほしいといわれて図書館で借り出していたことが発端でした・・・・。
そして、四方堂に通信販売でこの本上下揃え８０００円を注文してしまいました。
ラグランジュのインタポレーション公式を見ているとこの本を読めば
長年の懸案モーメント問題がすべて説明できそうな気がしてしまいましたから。
掛谷はディテールがないのです。ものすごい直観力で力ずくなのです。おそらく現代的な
アイディア（作用素論）を用いて磨きをかければ、きれいに証明がやり直せる。
いい定理が作れると思うのです。
（３）
行列の場合
T^*T-TT^*は非正で固有値は非負でその和トレースは非負だが
行列積のトレースが積の交換について不変であるから
T^*T-TT^*のトレースはゼロであり、和がゼロということは
すべての固有値がゼロとなりもともと
T^*T-TT^*がゼロ行列となってしまい
Tは正規行列となる。
すなわち行列のばあい、ハイポ正規なら正規である。
要点は、Toeplitz正規行列の場合、タイプI、タイプII のいずれかなのだが
Toeplitz正規作用素の場合タイプIになることをHalmosは示したが
奇妙なのは、タイプIIがでてこないことである。これは、作用素のほうが
行列を一般化していないのではないか？
あるいはToeplitz Operator と Toeplitz Matrix にはギャップがあることになるのだが
これもHalmosの書いていることと矛盾している。（おそらく、ぼくの思い違い、しかし・・・）
古田＠数学です。
ハイポ正規性と正規性について、
Hilbert
space H 上のコンパクト作用素に対しては
ハイポ正規性と正規性は同値となることが知られています。
よって、行列についてもハイポ正規性と正規性は同値になります。
行列の場合の証明は
等式 T^*T - TT^* \geq 0 の両辺のトレースをとればよいです。
R.M.Gray, 2001,
Toeplitz and Circulant Marices: A Review
a report
http://ee.stanford.edu/~gray/toeplitz.pdf
Caixing Gu 2002,
On a Class of Jointly Hyponormal Toeplitz Operators,
Transaction of AMS. 1-24
In order to study Hyponormal
Operators, I collected the following papers:
Brown Halmos,1963
Algebraic Properties of Toeplitz opertors
J. fur Reine and
Arch.Math,vol.213,89-102
----------------------------------
T.Ito ; T.K.Wong,1972
Subnormality and quasinormality of Toeplitz operators
Proc.AMS,157-164
--------------------------------------
Amemiya,
On quasinormal Toeplitz operatorsProc.AMS,1975,254-258
----------------------
1996
Hyponormality and spectra of Toeplitz
operators
Trans.AMS,vol.348,4153-4174
-----------------------------
1999
Hwang,I.S;Kim,I.H;Lee,W.Y
Hyponormality of Toeplitz operators with
polynomial symbols
Math.Annalen,313,247-261
-----------------
Subnormality and k-Hyponormality of Toeplitz Operators:
A Brief Survey and Open Questions
by Curto,Raul and Woo Young Lee
Banach Center Publications, volme**
Institute of
---------------------------------------
2001
Reduced Cowen Sets
Raul E. Curto and Woo Young
Lee
http://nyjm.albany.edu:8000/j/2001/7-13.html
---------------------------------
2002
IN SUG HWANG and WOO YOUNG LEE
Hyponormality of Trigonometric Toeplitz
Operators
Transaction of AMS,vol.354,no.6,2461-2467
Lecture Note:
Functional
Analysis Douglas N. Arnold,Penn State Univ.1997 Spring.
Complex Analysis Douglas N. Arnold,Penn State Univ.1997
Spring
By N.L.Carothers
Mersenne
Twister Lecture by
Matsumoto
http://www.soi.wide.ad.jp/class/20010000/slides/03/
A Short Course on
Approximation Theory
by N.L.Calother,
Lecture Note Math.682,1998, 1-155
On 3/16, I have read. This is one
of the great lectures I ever read.
2002/03/10
Subnormality and
k-Hyponormality of Toeplitz Operators:
ABrief
Survey and Open Questions
by Curto,Raul and Woo Young Lee
Banach Center Publications, volme**
Institute of
Now reading
Hyponormality of Trigonometric Toeplitz
Operators
IN SUG HWANG and WOO YOUNG LEE
Transaction of AMS,vol.354,no.6,2461-2467
Reduced Cowen Sets
Raul E. Curto and Woo Young
Lee
http://nyjm.albany.edu:8000/j/2001/7-13.html
by M.I.Ostrovskii
1-8
A note on lp-norms
Behrehard,Olga Katkova, Anna Vishnyakova
On the Distribution Singular Values of Toeplitz
Matrices
Milutin R.Dostanic
Proc.AMS vol.130,no.6,2001
Hausdorff Matrices and Composition Operators
Peros Galanopoulos and Aristomenis G.Sikakis
Illinois J. of Math.,vol.45,2001
Non-Commutative Clarkson Inequalities for Unitarily
Invariant Norms
Omar Hirzallah and Fuad Kittaneh
Pacific J. Math.,vol.202,no.2,2002
I have read lecture note
Functional analysis lecture notes
by T.B. Ward
School of mathematics,
平成14年2月4日
読まなければならない：
数学 ５４巻 １号 ２００２年１月 岩波書店
の極大イデアル空間の構造 泉池 啓司
P=NP問題 西野 哲郎
Riemann 予想 本橋 洋一
図書館でコピーするもの
Babenko,K.I.1986, On Toeplitz and Hankel Matrices, Usp.Mat.Nauk,vol.41,no.1(247),pp.171-178
Qazi I. Rahman, G. Schmeisser, L p inequalities for entire functions of exponential type,
Trans. Amer. Math. Soc. 320 (1990), 91--103
岩波数学
関数環とその関連分野特集（1976年1月）
Banach環概説：竹之内 脩 1-9
荷見 守助：不変部分空間の理論47-57
数学 ５４巻 １号 ２００２年１月 岩波書店
の極大イデアル空間の構造 泉池 啓司
かなえてほしい、夏のあこがれ
ｂｙ