N. Dunford, J.T. Schwartz, Linear Operators, Part I: General Theory, Wiley (1957). Home/Search Document Not in Database Summary Related Articles Check |
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Ann. Henri Poincare 2 (2001) 1065 -- 1097 - Birkhauser Verlag Basel (Correct)
....by H2, has exponential decay with mass rates # i #, thus controlling the sum in x.Thedq integration in (5.19)is an integral as in (5.7) being finite because the integrand is bounded if we fix k 0 D 1 . The last claim of Lemma 4.2 (a)is a well known fact about compact operators (see, f.i. [18], Lemma 13) We have already proven parts (a) and (c) of Lemma 4.2. For the statement (b)of Lemma 4.2 note that, under H3, R is given by R = R # 0 (1I # K 1 R # 0 ) 1 ,whereR # 0 : R 1 0 # 1) 1 .Itiseasytoverify(Lemma 4.1 in [2] that R # 0 is given by the kernel R # 0 (k, p, q) R 0 ....
N. Dunford and J T. Schwartz, Linear Operators. Part I: General Theory, Interscience, New York, 1958.
The Large Deviation Principle For Stochastic Processes - Arcones (2002) (Correct)
....uniformly equicontinuous functions in (T , #) Since for each t T , I t is a good rate function, for each 0 # c z(t) I(z) # c u : I t (u) # c #. So, T ) I(z) # c is a set of uniformly bounded functions. The Arzela Ascoli theorem (see for example Theorem IV.6. 7 in [16]) implies that (T ) I(z) # c is a compact set of l (T ) We may apply this theorem even when (T , #) is a totally bounded pseudometric space and not a compact space because identifying the points which are at a zero distance (see Problem 2C in [34] we may assume that (T , #) is a metric ....
....isometrically embedded as a dense subset of the complete metric space consisting of the Cauchy sequences in this space (see for example Theorem 24.4 in [34] The considered functions can be extended as functions in the completion by the principle of extension by continuity (see Theorem I.6. 17 in [16]) Lemma 3.1 is proved. We call a function #: T T a finite partition function if for each T , #(#(t) #(t) and the cardinality of #(t) T is finite. Let #(T ) and A j = t # T : #(t) t j for 1 # j # m, then A 1 , Am is a partition of T . Finite partition ....
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Dunford N., Schwartz J. T. Linear Operators. Part I: General Theory. New York: Wiley, 1988, 858 p.
Perron-Frobenius spectrum for random maps and its approximation - Blank (2001) (Correct)
....to the set of regular elements, i.e. to the points z 2 C such that the resolvent (zI P) of the operator is de ned in the entire space and hence is bounded. The maximal (on modulus) element of the spectrum is called the spectral radius: B (P) supfjzj : z 2 sp B (P)g: As it is well known [8] the spectral radius can be calculated by the following formula: B (P) lim B Browder [5] introduced the notion of essential spectrum ess sp B (P) of a bounded linear operator P as a union of the elements of the spectrum z 2 sp B (P) such that at least one of the following properties ....
N. Dunford, J.T. Schwartz, Linear operators, Part 1: General Theory, Wiley, 1957.
Weyl Function And Spectral Properties Of Self-Adjoint.. - Brasche, Malamud.. (Correct)
....V : fV h (x iy) 0 y 1g L ( a; b) of non negative functions has equicontinuous absolutely continuous integrals, that is mes(E)#0 E V h (x iy) dx = 0 (4.18) uniformly in y 2 (0; 1) It follows from (4.16) that the set V is bounded in L ( a; b) This fact and (4. 18) yield (see [12]) the sequentially weak compactness of V in L ( a; b) Therefore, for each sequence fy n g n=1 tending to zero there exists a subsequence fy n k g such that V h (x iy n k ) weakly converges in L ( a; b) as k 1, that is, there is an element f h 2 L ( a; b) such that for each ....
N. Dunford and J. T. Schwartz, Linear operators. Part I: General Theory, John Wiley & Sons, New York 1988.
Unknown - (1998) (Correct)
....0 (jkj [ 2 ] 1) then there exist M 0 and 2 C c such that u t (1 Gamma ) 2 FL and ku t (1 Gamma )kFL 1 M (1 t ) for t 0. Finally, let jAj P n j=1 A j and C ff = 1 jAj (ff 2 R) as fractional powers. Then C ff = 1 j Delta j (A) 2 B(X) for ff 0 (see [5]) and (R(C ff ) D(P (A) for ff m (cf. 15, 24] Relating to P (A) as the generator of a C ff regularized semigroup (see x3 below) we have the following result of wellposedness of (1.1) cf. 4, 24] Lemma 1.2. Let a 0, and M ff , ff be suitable constants depending on ff. a) If P ....
N. Dunford and J.T. Schwartz, Linear Operators, Part I: General Theory, Interscience, New York, 1960.
Layout Problems on Lattice Graphs - Díaz, Penrose, Petit, Serna (Correct)
....process on the in nite lattice Z 2 , with clusters in this latter process denoted e C x . minla(L m;p ) m 2 = m 2 X x2Vm minla(C x ) jC x j = m 2 X x2Vm minla( e C x ) j e C x j m 2 X x2Vm minla(C x ) jC x j minla( e C x ) j e C x j : 1) Using theorem VII.6. 9 from [6] and the Kolmogorov zero one law, m 2 X x2Vm minla( e C x ) j e C x j Pr E p minla( e C 0 ) j e C 0 j # : Writing Vm for the set of x 2 Vm with lattice neighbors in Z 2 nVm , we get m 2 X x2Vm minla(C x ) jC x j minla( e C x ) j e C x j 2m 2 ....
N. Dunford and J. Schwartz. Linear Operators. Part I: General Theory. Interscience Publisher, New York, 1958.
Layout Problems on Lattice Graphs - Díaz, Penrose, Petit, Serna (1999) (Correct)
....lattice Z 2 , with clusters in this latter process denoted # C x . minla(L m,p ) m 2 = m 2 # x#Vm minla(C x ) C x = m 2 # x#Vm minla( # C x ) # C x m 2 # x#Vm # minla(C x ) C x minla( # C x ) # C x # . 1) Using theorem VII.6. 9 from [6] and the Kolmogorov zero one law, m 2 # x#Vm minla( # C x ) # C x Pr # E p # minla( # C 0 ) # C 0 # . Writing #Vm for the set of x # Vm with lattice neighbors in Z 2 Vm , we get m 2 # x#Vm # # # # # # minla(C x ) C x minla( # C x ) # C x ....
N. Dunford and J. Schwartz. Linear Operators. Part I: General Theory. Interscience Publisher, New York, 1958.
A two space dimensional semilinear heat equation.. - Albeverio, Haba, Russo (1999) (2 citations) (Correct)
....framework is that they are only generalized in space but ordinary in time. The correct term should be: algebra of simplified Fr echet valued random tempered generalized functions. The following description is partly inspired by ch. 4 of [C1] and x12 of [O1] We first recall, see for instance [DS], ch. II, that a Fr echet space F is a linear topological space, complete, equipped with a homogeneous metric. Examples of such spaces are S(IR d ) C k (IR d ) for k 0. Given a closed subset B of IR d , S(B) will be the Fr echet space of the functions in S(IR d ) restricted to B. ....
....values in C(B) or more generally elements of trace type j : B Theta S(IR 2 ) C, that it to say such that (1. 4) ff (t j(t; ff) is a linear continuous functional, i.e. a vector valued distribution from S(IR 2 ) to C(B) The space of such j is a Fr echet space (F space in the sense of [DS], ch. 2) We remark in particular that for any compact B loc ae B and bounded subset S of S(IR 2 ) sup ff2S sup t2B loc jj(t; ff)j 1 A tempered distribution j 2 S 0 (IR d 2 ) is said to have the trace property with respect to the closure of an open subset B of IR d if (1:5) 8t 2 B; ....
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N. Dunford, J.T. Schwartz, Linear operators, Part I: General theory, Publishers Inc., New York (1967).
Decay of Correlations for Certain Quadratic Maps - Young (1992) (15 citations) (Correct)
....large, there is a finite rank operator Q with kP N Gamma Qk 1. This second lemma tells us that outside of some disk of radius 1; oe(P ) consists of at most a finite number of points j 1 ; j , and that the projection corresponding to each j i has a finite dimensional range ([DS] VIII 8) No j i 2 S 1 can be a pole of order 1, for that would violate sup n kP n k 1. This completes the proof. Sublemma 5.1a. sup B2fi N VB (g N ) 1 8N . Proof. Since jf 0 xj ffi 8x and f maps each element of fi to at most 3 elements of fi, we have X B2fi N BaeJ 1 V B ....
Dunford & Schwartz, Linear operators, Part I: general theory (1957).
Absolutely Continuous Invariant Measures For Random Maps With .. - Góra, Boyarsky (2000) (Correct)
....(functions of x) If invariant densities f (n) of random maps T (n) # 1 , # K ; p (n) 1 , p (n) K , n = 1, 2, exist and converge weakly in L 1 to a density f # , then f # # A # . Proof. If f (n) # f # weakly in L 1 , then by Mazur s Theorem ([DS], V.3.14. there exists a sequence h (n) of convex combinations of f (n) s which converges in the L 1 norm to the density f # . Since A # is convex each h (n) is an invariant density of a random map T (n) # 1 , # K ; q (n) 1 , q (n) K , for some ....
Dunford, N., and Schwartz, J.T., Linear Operators, Part I: General Theory, Interscience Publ. Inc., N.Y., 1964.
Convergence Of A Time-Stepping Scheme For Rigid Body Dynamics And .. - Stewart (1998) (3 citations) (Correct)
....2 R m , z 2 R n such that z 0; g(x; z) 0; z T g(x; z) 0; h(x; z) 0: Convergence of a time stepping scheme for rigid body dynamics 5 2.1. Measure differential inclusions. In general, this system does not have solutions involving impacts unless ( Delta) is allowed to be a distribution [17, 24] or a vector measure [10, 16] The best known example is the Dirac ffi function , which is a unit impulse concentrated at time zero. These impulses cannot be understood in terms of their values, but rather in terms of integrals that contain them. A distribution, vector measure or impulse must ....
N. Dunford and J. T. Schwartz. Linear Operators, Part I: General theory. Wiley Interscience, New York, 1957.
Stability of the spectrum for transfer operators - Gerhard Keller Universitat Self-citation (Operators) (Correct)
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N. Dunford, J.T. Schwartz, Linear Operators, Part I: General Theory, Wiley (1957).
On Transfer Operators for Continued Fractions with.. - Jenkinson, Gonzalez.. (2002) Self-citation (Operators) (Correct)
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N. Dunford & J. T. Schwartz, Linear Operators. Part I: General Theory, Interscience, New York, 1957.
On Transfer Operators for Continued Fractions with.. - Jenkinson, Gonzalez.. (2001) Self-citation (Operators) (Correct)
....multiplicity of is the same for both A and B) Now K I; L 2 (m I ) L 2 (m I ) 20 O. JENKINSON, L.F. GONZALEZ, AND M. URBA NSKI is trace class by Proposition 5, hence so is the operator A, by Theorem 1 (b) In particular A is compact, so that R ( A) is nite dimensional ([15], Thm. 7.4.5) Therefore equation (10) together with the injectivity of , implies that is an isomorphism between the nite dimensional generalised eigenspaces R ( A) and R ( B) Using (9) and the fact that B commutes with ( B) we see that the restrictions BjR ( B) and AjR ....
N. Dunford & J. T. Schwartz, Linear Operators. Part I: General Theory, Interscience, New York, 1957.
Stability Indices of Infinite-Dimensional Discrete Inclusions - Wirth (1997) (Correct)
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N. Dunford and J. Schwartz. Linear Operators, Part I: General Theory. Interscience, New York, (1958).
Exponential Stability of Families of Linear Delay Systems - Wirth (Correct)
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N. Dunford and J. Schwartz. Linear Operators, Part I: General Theory. Interscience, New York, (1958).
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 43, NO. 9.. - Systems Via Convex (Correct)
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N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory. New York: Wiley, 1967.
Convergence of Restarted Krylov Subspaces to Invariant.. - Beattie, Embree, Rossi (2001) (1 citation) (Correct)
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N. Dunford and J. Schwartz, Linear Operators, Part I: General Theory, Wiley, New York, 1971.
Convolution Complementarity Problems with Application to Impact.. - Stewart (Correct)
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N. Dunford and J. T. Schwartz, Linear Operators, Part I: General theory, Wiley Interscience, New York, 1957.
Linear Ode's For Describing - Sigma- Delta-Modulators Filter (Correct)
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Dunford, N.; Schwartz, J.T., Linear Operators, Part I General Theory, Wiley, New York, 1988.
The Large Deviation Principle for Stochastic Processes. II - Arcones (2003) (Correct)
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Dunford N., Schwartz J. T. Linear Operators. Part I: General Theory. New York: Wiley, 1988, 858 p.
Unknown - (Correct)
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N. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory, 2 printing, Interscience Publishers, New York 1964.
A Unique Subjective State Space for Unforeseen Contingencies - Dekel, Lipman, Rustichini (1997) (2 citations) (Correct)
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Nelson Dunford and Jacob T. Schwartz (1958): Linear Operators, Part I: General Theory, Wiley: New York, NY.
Statistical Properties of Dynamical Systems with Some Hyperbolicity - Young (1996) (32 citations) (Correct)
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Dunford and Schwartz, Linear operators, Part I: General Theory, 1957.
Convergence Theorems for Some Layout Measures on Random .. - Diaz, Penrose, Petit.. (Correct)
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N. Dunford and J. Schwartz. Linear Op erators. Part I: General Theory. Interscience Publisher, New Y ork, 1958.
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