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The Kato theorem, or Kato's cusp condition (after Japanese mathematician Tosio Kato), is used in computational quantum physics. It states that for generalized...

matrix exponential of A. The Lie–Trotter product formula and the Trotter–Kato theorem extend this to certain unbounded linear operators A and B. This formula...

{\displaystyle K_{n}^{M}(k)/\ell } . The norm residue isomorphism theorem (or Bloch–Kato conjecture) states that for a field k and an integer ℓ that is invertible...

Neumann theorem O'Connor, John J.; Robertson, Edmund F., "Tosio Kato", MacTutor History of Mathematics Archive, University of St Andrews "Tosio Kato (1917—1999)"...

countable, then T is strongly stable. Hille–Yosida theorem Lumer–Phillips theorem Trotter–Kato theorem Analytic semigroup Contraction (operator theory)...

the trace-class operators, the situation is quite different. The Kato–Rosenblum theorem, proved in 1957 using scattering theory, states that if two bounded...

Geometry". Kato has published several books in Japanese, of which some have already been translated into English. He wrote a book on Fermat's Last Theorem and...

became a research associate to Hiroshi Fujita (known for the Fujita-Kato theorem) at the University of Tokyo. There in 1985 he received his Doctorate...

theorem is a result from operator and matrix theory about the representation of a sum of two bounded, linear operators (resp. matrices). The theorem was...

topics) listed below. Birkhoff–von Neumann algorithm Birkhoff–von Neumann theorem Birkhoff–von Neumann decomposition Dirac–von Neumann axioms Koopman–von...

Remmert–Stein theorem, introduced by Reinhold Remmert and Karl Stein (1953), gives conditions for the closure of an analytic set to be analytic. The theorem states...

Blodgett Katherine Freese Katherine McAlpine Katherine Sopka Kathy Sykes Kato theorem Katsunori Wakabayashi Kaufmann (Scully) vortex Kautsky effect Kauzmann...

converse to Herbrand's theorem (the so-called Herbrand–Ribet theorem). Karl Rubin found a more elementary proof of the Mazur-Wiles theorem by using Kolyvagin's...

 3). Conrad (2008), Theorem 2; Koblitz (1993), Exercise 3, p. 5. Dickson (1920). Koblitz (1993), Proposition 19, pp. 46–47; Kato & Saitō (2000). Edwards...

72 (3): 936–938. doi:10.1139/v94-121. ISSN 0008-4042. T. Kato (1950). "On the Adiabatic Theorem of Quantum Mechanics". Journal of the Physical Society of...

equal to its conjugate transpose A∗. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this...

000 prize for the first correct proof. Mordell (1922) proved Mordell's theorem: the group of rational points on an elliptic curve has a finite basis....

Appendix A. Hille and Phillips, Theorem 11.4.1, p. 341 Dunford and Schwartz, Vol I, Lemma 6, p. 568. Hille and Phillips, Theorem 4.8.2, p. 126 Taylor, p. 515...

field Dirichlet's unit theorem, S-unit Kummer extension Minkowski's theorem, Geometry of numbers Chebotarev's density theorem Ray class group Decomposition...

group has plenty of applications, such as the Grothendieck–Riemann–Roch theorem. Intersection theory is still a motivating force in the development of...