Symmetric Kernels

Ram P. Kanwal
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Ram P. Kanwal: Pennsylvania State University, Department of Mathematics

Chapter Chapter 7 in Linear Integral Equations, 1997, pp 146-180 from Springer

Abstract: Abstract A kernel K (s, t) is symmetric (or complex symmetric or Hermitian) if 7.1.1 % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiaacI % cacaWGZbGaaiilaiaadshacaGGPaGaeyypa0Jaam4saiaacQcacaGG % OaGaamiDaiaacYcacaWGZbGaaiykaiaacYcaaaa!41E5! $$K(s,t) = K*(t,s),$$ where the asterisk denotes the complex conjugate. In the case of a real kernel, the symmetry reduces to the equality 7.1.2 % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiaacI % cacaWGZbGaaiilaiaadshacaGGPaGaeyypa0Jaam4saiaacIcacaWG % 0bGaaiilaiaadohacaGGPaGaaiOlaaaa!4139! $$K(s,t) = K(t,s).$$

Date: 1997
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DOI: 10.1007/978-1-4612-0765-8_7

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