Quadratic inequalities deduced from the theory of reproducing kernels

✍ Scribed by Saburou Saitoh

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 319 KB
• Volume: 93
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(87)90322-3

✦ Synopsis

A typical result given in this paper is as follows: For an N X N positive definite Hermitian matrix A and for any vector x E CN, we obtain the inequality (expx)*(expA-')-l(expx) <exp(x*Ax), where, for x=(x1,x2 ,..., xN)r, expx=(exprl,expx2 ,..., expxN)r and for A= 11~~~11, expA = Il(exp a,,)ll. We deal with inequalities of this type in a more general situation by using the theory of reproducing kernels.