Yosida, K.: Functional Analysis. 6th ed., NewYork: Springer, 1980 Communicated by J. L. Lebowitz  Home/Search Document Not in Database Summary Related Articles Check |
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Evolution Equations and Geometric Function Theory in J*-Algebras - Elin, Harris, al. (Correct)
....group) of composition operators on g Hol(D; X) This follows from the observation that L(t)I D = S(t) 1.1.13) T g I D = g: 1.1.14) Moreover, using the exponential formula representation for the linear semigroup: L(t)f = T g f = exp [ tT g ]f; 1.1. 15) see, for example, [54, 36]) 1.1.13) and (1.1.14) we have S(t) g I D = exp [ tT g ]I D : 1.1.16) In other words, a T continuous semigroup of holomorphic self mappings on a bounded domain can be represented in exponential form by the holomorphic vector eld corresponding to its generator. 12 Another ....
K. Yosida, Functional Analysis, Springer, Berlin, 1968. 57
Linear Structures for Concurrency in Probabilistic.. - Di Pierro, Wiklicky (2001) (Correct)
....on them. In functional analysis i.e. in dealing with in nite dimensional vector spaces a common way to introduce a topology on a linear space is by means of a norm, k k and its corresponding metric d( x; y) k x; yk) The topology induced by such a metric is called norm topology [25,71,40]. A nice feature of nite dimensional linear spaces is the fact that all norm topologies are equivalent [26] Therefore, one can refer to the topology of V(State) and L(V(State) without specifying any particular norm. In the in nite case, di erent norms give rise to di erent topologies and it ....
....on the structure of the agent A and the fact that under the hypothesis that p i s are normalised the simplex S(L) is closed with respect to all the operations on the right hand side of the equations in Figure 6. 2 Continuity of : The continuity of follows from the following classical result [71,59]: Theorem 4.14 A linear map T : V 7 W from a normed vector space (V; k:k V ) into another normed vector space (W; k:k W ) is continuous if and only if it is bounded, i.e. 9c 0 : kT(x)kW c kxk V Proposition 4.15 The operator de ned in Figure 6 is continuous. Proof. It is clear that ....
Yosida, K., \Functional Analysis," Springer Verlag, Berlin { Heidelberg { New York, 1980.
Diffusion Approximation of a Neutron Transport Equation.. - Protopopescu, Thevenot (2003) (Correct)
....that TR = 1, then = 4a. Therefore TR does not admit other generalized eigenfunctions beyond the constant functions. The same proof holds for the adjoint of TR de ned by R = x C D(T R ) D(TR ) From Lemma 2 and from the theory of isolated singularities of the resolvent (see [Y]) we deduce the Fredholm alternative for the operator TR and the following proposition. Let f and g be in L (0; 1) The system C = 0 on ( a; a) 1; 1) a; a; f( 0 (a; a; g( 0 (6) admits a solution in W g( f( ....
.... (x; dxd = 0: 8) According to Lemma 2, 0 is an algebraically simple eigenvalue of TR and of its adjoint, TR , associated with the constant eigenvector. Let us notice that P is the spectral projection associated with the eigenvalue 0 of TR . Since P is bounded and ker(P ) R( TR ) see [Y]) then the range of TR , R(TR ) is a closed subspace. Therefore R(TR ) R(TR ) ker(T R ker(T R ) Now let be the extension of f and g as in Lemma 1. Then, satis es Equation (6) if and only if the function = satis es the system C = x C on ( a; a) ....
K. Yosida. Functional analysis. Springer Verlag, Berlin, 1974. 29
Internal and External Stability and Robust Stability.. - Yamamoto, Hara (1991) (Correct)
....the same output #(x( t) 11 Now #(q x) is clearly equal to #(# x) Since ord #(# q 1 ) ord(q 1 ) by hypothesis, ord #(# x) ord #(q x) Thus the regularity of # # t x is at least one higher than that of x. Therefore, t (L 2 [ a, 0] By Rellich s theorem (Yosida [1980]) this implies that # # t is a compact operator. Therefore, its adjoint # t is also compact. # Proof of Theorem 3.5 Since # t is compact for any t T, it is well known (e.g. Zabczyk [1976, Lemma 1] see also Pruss [1984] that the semigroup # t has the spectrum determined growth property, i.e. ....
K. Yosida, Functional Analysis, Springer, 1980.
Some Remarks on Hamiltonians and the Infinite-Dimensional - One Block Problem (Correct)
....in H . However, H(m) is not invariant under T (t) This is why we need to invoke # to define the compressed right shift in H(m) as in (3) However, it is invariant under the dual semigroup T # (t) which is the left shift semigroup. It is easy to see that its infinitesimal generator T # (cf. [16]) is the di#erential operator d dt . Since the symbol of W # c is given by W(s) see the proof of Proposition 2.7) the correspondence # = W # c w is represented in the state space form by substituting d dt for the realization ( A ,B ) as follows: dt p = p C (25) 7 This is ....
K. Yosida, Functional Analysis, Springer, 1980.
On Fictitious Domain Formulations for Maxwell's Equations - Dahmen, Klint, Urban (2002) (Correct)
....any U 2 V , ckUk V kLUk V 0 CkUk V : 2.29) The characterization of well posedness for real valued bilinear forms a( and b( in terms of inf sup conditions is due to F. Brezzi (see [3, Thm. II.1. 1] It s counterpart for complex valued bilinear forms reads as follows (see [3] and [17, 23, 25]) Theorem 2.3 De ne ker(B) fv 2 X : Bv = 0 in M g. The saddle point problem (2.28) is well posed if and only if the following conditions hold for some positive constants ; 0: kukX kvk X 0; 2.30) kukX ; kvk X 0; 2.31) p2M u2X jb(u; p)j kukX kpk M 0: ....
K. Yosida, Functional Analysis, Springer Verlag, 6th Edition, 1980. 18
On Second-order Properties of the Moreau-Yosida Regularization.. - Meng, Zhao Self-citation (Yosida) (Correct)
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Yosida, K., Functional analysis, Springer Verlag, Berlin, 1964.
On Smoothness of the Moreau-Yosida Regularization of a.. - Zhao, Meng Self-citation (Yosida) (Correct)
....Lagrangian dual of problem (1) as follows: minf (v) j v 2 R (Ax a) j x 2 Fg: 3) A substantial obstacle in solving problem (2) is that the function (v) is nondi erentiable. To overcome this, we convert problem (2) into another convex problem by using the so called Moreau [10] Yosida [17] regularization of , associated with M , de ned by minf (v) j v 2 R (v) min w2R m f (w) 1 jjw vjj M g; v 2 R : 5) where M is a symmetric positive de nite m m matrix and for any v 2 R , let kvk M = Mv: It is known that the set of minimizers of the problem (4) is ....
K. Yosida, Functional analysis, Springer Verlag, Berlin, 1964.
Commun. Math. Phys. 212, 105 -- 164 (2000) - Communications In Mathematical (Correct)
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Yosida, K.: Functional Analysis. 6th ed., NewYork: Springer, 1980 Communicated by J. L. Lebowitz
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K. Yosida. Functional analysis. Springer-Verlag, Berlin, 6th edition, 1980.
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Yosida, K., "Functional analysis," Springer-Verlag, Berlin, 1965. 23. Zen'isek, A., The finite element method for nonlinear elliptic equations with discontinuous coefficients, Numer. Math. 58 (1990), 51--77. 24. Zen'isek, A., "Nonlinear elliptic and evolution problems and their finite element approximations, " Academic Press, London, 1990. 24
Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra - Jean-Pierre Dedieu Myong-Hi (Correct)
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Appendix A - Discretisation Integral Equations (Correct)
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K. Yosida. Functional Analysis. Springer, Berlin, 1974. 22
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Yosida, K.: Functional Analysis. 6th ed., Springer, Berlin, 1980
Networks and the Best Approximation Property - Girosi, Poggio (1989) (56 citations) (Correct)
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K. Yosida. Functional Analysis. Springer, Berlin, 1974. 16
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