Geodesic
On P.A. Shirokov's Curve and Theorems of Hausdorff and Dines
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 51-53
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We discuss relations between geometric results obtained by P. A. Shirokov in 1930-s and classical theorems of F. Hausdorff and L. Dines.
Keywords: quadratic form, numerical range, boundary curve. 
@article{UZKU_2009_151_4_a4,
     author = {M. Yu. Kokurin},
     title = {On {P.A.~Shirokov's} {Curve} and {Theorems} of {Hausdorff} and {Dines}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {51--53},
     year = {2009},
     volume = {151},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a4/}
}
TY  - JOUR
AU  - M. Yu. Kokurin
TI  - On P.A. Shirokov's Curve and Theorems of Hausdorff and Dines
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2009
SP  - 51
EP  - 53
VL  - 151
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a4/
LA  - ru
ID  - UZKU_2009_151_4_a4
ER  - 
%0 Journal Article
%A M. Yu. Kokurin
%T On P.A. Shirokov's Curve and Theorems of Hausdorff and Dines
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2009
%P 51-53
%V 151
%N 4
%U http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a4/
%G ru
%F UZKU_2009_151_4_a4
M. Yu. Kokurin. On P.A. Shirokov's Curve and Theorems of Hausdorff and Dines. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 51-53. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a4/

[1] Godunov S. K., Sovremennye aspekty lineinoi algebry, Nauch. kniga, Novosibirsk, 1997, 390 pp. | Zbl

[2] Khalmosh P., Gilbertovo prostranstvo v zadachakh, IO NFMI, Novokuznetsk, 2000, 348 pp.

[3] Dines L., “On the mapping of quadratic forms”, Bull. Amer. Math. Soc., 47:6 (1941), 494–498 | DOI | MR | Zbl

[4] Shirokov P. A., “O granitse oblasti znachenii prisoedinennoi formy”, Izv. Fiz.-matem. o-va pri Kazan. un-te. Ser. 3, 7, 1936, 89–96 | Zbl

[5] Shirokov P. A., Izbrannye raboty po geometrii, Kazan. gos. un-t, Kazan, 1966, 432 pp. | MR

[6] Gau H.-L., “Elliptic numerical ranges of $4\times4$ matrices”, Taiwan. J. Math., 10:1 (2006), 117–128 | MR | Zbl

[7] Nakazato H., Bebiano N., Providencia J., “The $J$-numerical range of a $J$-Hermitian matrix and related inequalities”, Linear Algebra Appl., 428:11–12 (2008), 2995–3014 | DOI | MR | Zbl

[8] Joswig M., Straub B., “On the numerical range map”, J. Austral. Math. Soc. Ser. A, 65:2 (1998), 267–283 | DOI | MR | Zbl

[9] Caston L., Savova M., Spitkovsky I., Zobin N., “On eigenvalues and boundary curvature of the numerical range”, Linear Algebra Appl., 322:1–3 (2001), 129–140 | DOI | MR | Zbl

[10] Bebiano N., Lemos R., da Providkncia J., Soares G., “On the geometry of numerical ranges in spaces with an indefinite inner product”, Linear Algebra Appl., 399 (2005), 17–34 | DOI | MR | Zbl

[11] Zachlin P., On the field of values of the inverse of a matrix, Dissertation, Case Western Reserve University, Cleveland, USA, 2007, 70 pp.

[12] Kippenhahn R., “Uber den Wertevorrat einer Matrix”, Math. Nachr., 6 (1951), 193–228 | DOI | MR | Zbl

[13] Kippenhahn R., “On the numerical range of a matrix”, Linear Multilinear Algebra, 56:1–2 (2008), 185–225 | MR | Zbl